The tread is the part you stand on and includes the nose - thickness of the tread.
In this picture, we sanded and finished the treads only. Note how they are now a lighter colour than the Riser and stringers? The old coating has yellowed and some people do not like this look, so it is more cost effective to paint the Side Stringers and Risers afterwards. See below.
Side stringers run down the wall, and in this picture, under the hand rails.
Not all staircases have side stringers.