It may be because i'm half asleep as I type this but I don't think either actually had a space station yet tho both were working on ones and may have launched the start of their stations right at the end of the season- it's been a few months since i've watched the show so details like that are eluding me.
There's a lot of jumping about, and definitely not a mission by mission timeline, but that sounds right. The Soviets appear to still be flying single man missions, and without further details I lean toward imagining something on the level of an LK version of the LM shelter being what's extending their stay.
The Americans have a base, but it's monolithic. I suspect the show created it with LESA in mind.
OTOH they also have a multi flight LM (honestly, I think it's less a real tech based decision than something that made a couple of scripts work better), and while no Lunar station is shown there is something kind of off about the architecture involved if there's no refueling station anywhere.
The next thing we know they've gone and built Sea Dragon... I think the writers are really fond of big dumb rockets and monolithic vehicles.