Well, no. F-15 is fighter which was later adapted as attack plane and is still mostly used as fighter. F-4 is multirole and as such was mostly used as attack plane if operators had dedicated fighters (Mirage III in Israel, F-14 is Iran). Same today if country has both F-15 and F-16 F-15 will be used as fighter and F-16 as attack plane (OK, that may be due to turn-around time)
Actually it's because most F-15s in service happen to be Single seaters, instead of Strike Eagles, and the only nations that operate the Strike Eagle and F-16 series together happen to be the US, Israel, Singapore and South Korea, all of which mostly operate them side by side, and/or prefer to use their Strike Eagles for penetration bombing with F-16s serving in an Air Superiority role (which better leverages the capabilities of the F-15E.)
Japan only operates the F-15J which isn't capable of Air to ground operations, and thus has to use their F-2s as attack aircraft, while the USAF and IAF use their C/Ds for Air Superiority and share CAP duties with their other aircraft while anything with multi-role capability is used as such.
Most of the time with the F-4, they'd use it for Attack missions because it was the only thing in their inventory capable of performing such a mission. Mostly because it was fucking huge and light enough to have a useful payload when fully fueled, and had an RIO/WSO in the back, which is a massive asset on both bombing missions and longer-duration CAP flights, (hence the development of the Tornado ADV.)
Meanwhile, with the F-20, it'd probably be a 1:1 replacement for pretty much everybody who was operating F-5s, or looking for a new, cheap more or less dedicated Interceptor, to replace their Lightnings and all of that, while thanks to the F-5's number of variants, the F-20 could've easily been adapted to do pretty much anything you wanted to do with it, faster and cheaper then the F-16, with the capability to support the Skyflash and Sparrow right off the bat.
It could easily work in a role complimentary to any other contemporary multirole fighter (and the Air National Guard wanted to use it like that,) save maybe the Gripen.
As a matter of interest the ONLY combat use of the Lightning was in the ground attack role, by the RSAF.
They also used it on a few occasions for photo reconnaissance. Said situation wasn't exactly combat, but fairly close to getting there.