NOTE: Three things to note here. First, I know what you're thinking and I agree. "STAB " is the silliest name for a government organization I have ever heard. Secondly, to help prevent confusion, I'm gonna start adding relevant links to posts. Thirdly, since the file on this is a jumbled mess of classified and non-classified data, I'm just going to write a summary --SΣ
The Supernatural Threat Analysis Bureau ("STAB") is a secret arm of the American government founded to combat and study supernatural forces. It's operatives will often act as if they are a part of the FBI or CIA, and indeed many of them believe that they do work for either of those. The most obvious of these are Fisk and his men (see here), though they are far from the only parts of the branch.
The SMSC is a branch of STAB that attempts to study and fight back against the PREs. Their codenames are taken from David Bowie songs.
There's also another branch, fairly recent, which was founded by a fellow named Rivers. Even the name of this branch is classified, though the organization has been nicknamed "The Sgt. Pepper's Lonely Hearts Club Band" after the Beatles. (See the blogs of Peter and John Rivers). Sgt. Pepper's tends to take a more directly aggressive approach to PREs.
There are other branches of STAB. But these are the important ones.
STAB has been known work with the international organization the PTC (see this), though for the most part the two groups tend to stay out of each other's way.
The Archive has sold information to all branches of STAB in the past.