Broach and button rifling is the same thing..........the other method is single point cut rifling.........unless you are talking about factory hammer forged.
Sorry forgot about polygonal
Uh, not hardly. A broached barrel, such as (was) done by Thompson Center is where the rifling is CUT by a single pass of a very expensive broach (a cutting tool that incrementally increases in cross-section) whereas button rifling swages, for lack of a better word, the rifling into the smooth bore by pulling or pushing a hardened button with the negative image of the rifle ground into it.
The button simply displaces metal, the broach cuts it away.