For the most part, everyone's hit it on the head.
The Big Two security firms are Knight Errant (Ares) and LoneStar (independent). LoneStar is the most 'common' beacuse in canon they own the municipal contracts for a majority of UCAS cities (Seattle in particular). LoneStar also takes corporate security contracts, and in that capacity, is not trying to enforce municipal law, rather to protect corporate interests.
KnightErrant has a subsidiary, called HardCorps that does more mercenary work than security work. Firewatch Teams are the elite of HardCorps and they figure prominently in "Burning Bright", the novel where they nuke Chicago (Cernak Blast).
Winter Security, NYPD Inc, NOPS, Atlantic Security, California Rangers, Lone Eagle, and your local organized crime group are all 'small-time' security groups that don't have Megacorporate Status (A or above), but still control large sections of a municipality/state security-wise. (LoneStar is a AA, and KE is a subsidary of an AAA, so it counts)
Renraku Red Samurai, Diaska Security, and other similar corporate security firms provide services only to their company. This is so they don't have to trust a compeditor with the security of their projects, but then again, they only do that for the really 'secure' operations. Also, the corporate groups have less of an enforcement duty and a protective duty: meaning they're more apt to shoot first, rather than try to apprehend. Also, with extraterratoriality (for the AAAs), they're enforcing corporate law, rather than national/municipal law, so they're free to shoot at will. However, also with extraterratorial matters, they'll be less likely to pursue you off corporate grounds (but they'll call the cops and let them know where they can shoot some big, bad, shadowrunners
)
Hope this wasn't too redundant!