Proscenium stage:
A proscenium theatre is what we usually think of as a "theatre".
Its primary feature is the Proscenium, a "picture frame" placed around the front of the playing area of an end stage
Arena Theatre:
A central stage surrounded by audience on all sides. The stage area is often raised to improve sightlines.
End Stage:
A Thrust stage extended wall to wall, like a thrust stage with audience on just one side, i.e. the front.
“Black Box” theatre, these are often big empty boxes painted black inside.