The logo for The Brig is not actually a brig. It is actually a full rigged ship. Full rigged ships have 3 square rigged masts.
There are 2 common uses of the term brig. The formal usage and another a lazy shorthand of brigantine. Both of these vessels have only 2 masts.
The brig has 2 square rigged masts while the brigantine only the forward mast is square.