A roundabout (mainly BrE) is a traffic circle - a junction of several roads consisting of a central (usually circular) island around which traffic moves in one direction.
A square is an open, typically four-sided, area surrounded by buildings.
Roundabouts exist to help car drivers get around. Squares are public spaces where people/pedestrians congregate (large ones may be called plazas).
Here's Old Street Roundabout in London, which could be transformed into a pedestrian square...
Although because of the shape some people might call this one a "squareabout"1, it's not yet a "square" because pedestrians can't really get to it.
1 There's a Holiday Inn just up the road from me that gives its address as The Squareabout, because it's in the middle of a large and relatively square roundabout.