Introduction
A boolean takes two solids that overlap and makes one solid out of them. There are three of them, and they differ only in which part of the overlap you keep:
Fuse
Fuse joins two or more solids into one. Everything the solids cover between them stays; the walls where they overlap disappear. Use it when bodies were kept apart on purpose — with the New tab, or because they came in from a STEP file — and now have to behave as one piece.
Common
Common keeps only the volume that lies inside every solid you pick, and throws the rest away. With two solids that is their overlap; with three it is the part all three cover.
Subtract
Subtract carves one solid out of another. The base is the solid you keep; the tool is the solid whose volume is taken away. Whatever the tool occupied becomes a hollow in the base, and the tool itself is gone.