It is possible that FSD Beta is the testing of the autonomous stack but that the public release of "autosteer on city streets" will be a stripped down version of FSD Beta. So, Tesla could release the parts of FSD Beta, as "autosteer on city streets", that they feel are reliable enough for full public release. It would allow them to say that they fulfilled the promise of releasing "autosteer on city streets" while they are still working to make FSD Beta reliable enough.
I can kind of see why Tesla calls it "autosteer on city streets". I think the idea is that "autosteer" does more than just steer to stay in the lane, "autosteer" can now turn the wheel all the way to 90 degrees to make turns at intersections. Additionally, "autosteer" is capable of steering to stay in the lane on residential streets with no lane lines or steer around parked cars.
Personally, I think of FSD Beta as "City NOA" as the main feature seems to be that it tries to navigate a route to get you to a destination that you put in. It does auto lane changes to stay on route, auto lane changes to pass slow traffic and makes turns at intersections to follow a route which is similar to what NOA does, except it does it for city streets instead of highways.
Interestingly, "Autosteer on city streets" used to be called "City NOA" back in 2019 when Tesla added a list of features to the FSD page. Personally, I feel like "autosteer on city streets" sounds less autonomous than "City NOA". It seems that Tesla might have changed the name to downplay the autonomy of the feature, perhaps to avoid criticism when the feature is released and it falls short of L4/L5 autonomy.