How is a play organized? (Two ways)?

Question

For example, a book is organized into units and chapters, I know that plays are organized into acts...but what other category?

Answer 1

A play can be unitary, that is undivided, taking place in one time period in one place. The Greeks stated this was the best and proper way to present the action, all else being reported, not shown.
The musical 1776 was originally done this way with changes marked by time cards.
A play can be marked out only in scenes, although in production it may be divided by an intermission. When a play is done in acts, there is an assumption that each act has a conclusion and the play concludes at the end. When written and marked in scenes, the author's thru line is assumed to go only to the final conclusion.
A few plays have been written where the only real division is location - the stage must support two or more locations/sets and the dialog goes on between and among people in the locations - think of Heaven, Earth, and Hell or Home and Battlefield (these are not titles, just location lists) - like an intercut movie.

Answer 2

Acts can be broken up into different scenes, either because the set changes or because time passes.