During the rather protracted process leading to the beginning of Space Shuttle development, NASA faced considerable opposition from other bodies in the government, particularly the OMB, who were concerned about the cost of developing a reusable or partially reusable spacecraft and skeptical that it would be as economically advantageous as NASA made it out to be. This skepticism led to a number of efforts to design a non-NASA shuttle which would, hopefully, be gentler on the budget than the typically grandiose NASA efforts. In particular, in 1971 President Nixon's science adviser, Edward David, convened a panel chaired by Alexander Flax to review the Shuttle's development and produce recommendations on how to proceed. When the Flax Committee issued an interim report in October 1971, they showed skepticism that the then-planned Shuttle program (which by that point generally resembled the OTL program) was achievable or practical (Flax noting that "members...doubt that a viable shuttle program can be undertaken without a degree of national commitment...analogous to that which sustained the Apollo program...certainly not now apparent"), and instead recommended that NASA develop a small "glider" that would be launched on top of a Titan IIIL (a wide-body version of the Titan), with a payload of perhaps 10,000 pounds, in effect a shuttle very much like the HL-42 (a development of the smaller HL-20 crew vehicle that was intended to give it a more significant payload). NASA, of course, didn't like the idea very much, nor did the Air Force (although the Air Force was never particularly happy with the shuttle anyways...)
Ultimately, of course, NASA was able to proceed with its preferred large shuttle by a combination of underhanded trickery (a larger but conceptually similar small OMB-designed shuttle was undermined when NASA assumed all the expensive bits would be located in an expendable booster, resulting in a high per-flight cost) and high-level political support (Caspar Weinberger, at that time the head of the Office of Management and Budget, was a fan of the space program; earlier, he had helped shield the Apollo program from cancellation of several late J-class missions). However, this decision was far from preordained; at several points, Fletcher (the then-administrator) and George Low (previously responsible for Apollo development following the Apollo 1 fire) considered cancelling the shuttle project altogether due to OMB pressure. It's plausible, especially if Air Force support was less forthcoming, that they might settle on a Flax-style glider shuttle as a compromise that will at least move them part of the way towards the end goal, much as NASA in the real world compromised for just a shuttle that they hoped could be used to sell a space station later on.
Supposing they did so, what would the consequences be? Certainly a Flax-style shuttle would be far simpler and easier to develop than the real shuttle; although the Titan IIIL would need to be developed, it had already been designed and most of the key, complex hardware already existed. None of the dramatic development difficulties experienced by the SSMEs would have occurred, since there would be no need to develop the SSMEs. On the whole, I suspect the first flight would take place as much as a year or two earlier than STS-1 actually did. It almost certainly would not have cost any more to operate, and might even have cost less given the far smaller size of the orbiter and the correspondingly smaller job of refurbishing it after flight, though the cost of handling the large Titan IIIL core and its extremely toxic hypergolic propellants might have eventually outweighed any savings on that end.
Safety-wise, although the Columbia accident would have been impossible (no external tank), the Challenger accident, or something much like it, would not have been, and could have been far worse given the fact that, as I mentioned, the Titan IIIL core used highly toxic hypergolic propellants instead of clean-burning liquid hydrogen and liquid oxygen. This serious Titan accident just a few months after Challenger proves the point. However, because the shuttle would be a spacecraft like Apollo or Soyuz instead of a launch vehicle, it could easily have been launched on a new launch vehicle designed to be safer and more reliable than the Titan IIIL (for example, something like one of the expanded Delta IVs). More importantly, due to the much smaller size of the orbiter and its likely positioning atop the Titan IIIL instead of on the side, it could have had a robust abort system built in, much like the HL-42; although a launch accident could have contaminated LC-39 and caused serious issues, it would have had a smaller chance of destroying the orbiter and killing the astronauts aboard than with the real shuttle.
Capability-wise, nothing serious would be lost; although the orbiter itself would not be able to independently carry space station modules, satellites, or other spacecraft into orbit, as events proved that was a largely illusory capability for the OTL shuttle, and the large capacity of the Titan IIIL would be a more than adequate substitute for government payloads. The Flax shuttle would be more than capable of acting as a space station logistics or rescue vehicle, or operating as an independent space station for short or medium-duration research flights like the OTL Spacelab or Spacehab flights, with other payloads flying on dedicated vehicles.
As far as broader effects go, I think the timeline e of pi and I have written is at least a good place to start, given that we have a similar change. First and perhaps foremost, without the "threat" of the orbiter "first striking" Moscow, Buran is very unlikely to go forwards as per OTL. Instead, a smaller shuttle might be built by Glushko (who still probably ends up getting control of the Soviet space program) to replace Soyuz and Progress for space station logistics, or there might not be any plans to replace those spacecraft at all. Without the promise and threat of the space shuttle in the late 1970s and early 1980s, the US commercial (such as it was) launch market at that time is probably healthier and tries harder to attract customers; and given that there won't be a Challenger-type failure that requires a lot of customers to suddenly find a new launch provider, Arianespace probably faces a much tougher row to hoe than IOTL, and is probably not as successful as OTL. They might still want to build their own mini orbiter, or they might not...
Ultimately, of course, NASA was able to proceed with its preferred large shuttle by a combination of underhanded trickery (a larger but conceptually similar small OMB-designed shuttle was undermined when NASA assumed all the expensive bits would be located in an expendable booster, resulting in a high per-flight cost) and high-level political support (Caspar Weinberger, at that time the head of the Office of Management and Budget, was a fan of the space program; earlier, he had helped shield the Apollo program from cancellation of several late J-class missions). However, this decision was far from preordained; at several points, Fletcher (the then-administrator) and George Low (previously responsible for Apollo development following the Apollo 1 fire) considered cancelling the shuttle project altogether due to OMB pressure. It's plausible, especially if Air Force support was less forthcoming, that they might settle on a Flax-style glider shuttle as a compromise that will at least move them part of the way towards the end goal, much as NASA in the real world compromised for just a shuttle that they hoped could be used to sell a space station later on.
Supposing they did so, what would the consequences be? Certainly a Flax-style shuttle would be far simpler and easier to develop than the real shuttle; although the Titan IIIL would need to be developed, it had already been designed and most of the key, complex hardware already existed. None of the dramatic development difficulties experienced by the SSMEs would have occurred, since there would be no need to develop the SSMEs. On the whole, I suspect the first flight would take place as much as a year or two earlier than STS-1 actually did. It almost certainly would not have cost any more to operate, and might even have cost less given the far smaller size of the orbiter and the correspondingly smaller job of refurbishing it after flight, though the cost of handling the large Titan IIIL core and its extremely toxic hypergolic propellants might have eventually outweighed any savings on that end.
Safety-wise, although the Columbia accident would have been impossible (no external tank), the Challenger accident, or something much like it, would not have been, and could have been far worse given the fact that, as I mentioned, the Titan IIIL core used highly toxic hypergolic propellants instead of clean-burning liquid hydrogen and liquid oxygen. This serious Titan accident just a few months after Challenger proves the point. However, because the shuttle would be a spacecraft like Apollo or Soyuz instead of a launch vehicle, it could easily have been launched on a new launch vehicle designed to be safer and more reliable than the Titan IIIL (for example, something like one of the expanded Delta IVs). More importantly, due to the much smaller size of the orbiter and its likely positioning atop the Titan IIIL instead of on the side, it could have had a robust abort system built in, much like the HL-42; although a launch accident could have contaminated LC-39 and caused serious issues, it would have had a smaller chance of destroying the orbiter and killing the astronauts aboard than with the real shuttle.
Capability-wise, nothing serious would be lost; although the orbiter itself would not be able to independently carry space station modules, satellites, or other spacecraft into orbit, as events proved that was a largely illusory capability for the OTL shuttle, and the large capacity of the Titan IIIL would be a more than adequate substitute for government payloads. The Flax shuttle would be more than capable of acting as a space station logistics or rescue vehicle, or operating as an independent space station for short or medium-duration research flights like the OTL Spacelab or Spacehab flights, with other payloads flying on dedicated vehicles.
As far as broader effects go, I think the timeline e of pi and I have written is at least a good place to start, given that we have a similar change. First and perhaps foremost, without the "threat" of the orbiter "first striking" Moscow, Buran is very unlikely to go forwards as per OTL. Instead, a smaller shuttle might be built by Glushko (who still probably ends up getting control of the Soviet space program) to replace Soyuz and Progress for space station logistics, or there might not be any plans to replace those spacecraft at all. Without the promise and threat of the space shuttle in the late 1970s and early 1980s, the US commercial (such as it was) launch market at that time is probably healthier and tries harder to attract customers; and given that there won't be a Challenger-type failure that requires a lot of customers to suddenly find a new launch provider, Arianespace probably faces a much tougher row to hoe than IOTL, and is probably not as successful as OTL. They might still want to build their own mini orbiter, or they might not...