They're char actually. Just look at the genus to find out. Char are genus salvelinus, such as arctic char salvelinus alpinus, brook trout, the state fish of my state salvelinus fontanalis or lake trout, salvelinus namaycush. Rainbow trout and cutthroat trout are actually a salmon, as they all belong to the genus onchorhynchus. Rainbow trout- Onchorhyncus mykiss, Cutthroat trout- Onchorhynchus clarki, Coho Salmon- Onchorhynchus kisutch. Brown trout are genus Salmo, the only trout of that genus in North America. The big difference between trout/salmon and char is scales. Brook trout and other char have extremely tiny scales, so that they just appear to have skin, not scales like the other "trouts".
This is like anything else, common names were decided on before science had genetics to know what is related to what, so they often call things something they in fact are not. Its no big deal though, I mean Char/trout/salmon, they all share very similar characteristics and are fun to catch.