I agree with both the comment and the answers here. But I want to add that both "These shoes are tight" and "These shoes are on the tight side" might both mean that the shoes are tight. "These shoes are on the tight side" is more polite though, because it is less direct.

These shoes are on the tight side means that the shoes are tighter than the speaker would like but they could be even tighter, which would be worse. Maybe they are willing to wear them anyway. These shoes are tight is straight to the point. They maybe less willing to try to wear the shoes then.

The first phrase is more affirmative. As though the shoes being tight is a fact. The second is more like you are saying the shoes are a little tight. On the tight side is like they are more tight than shoes which arent tight, but not totally tight just a little 'on the tight side'