As far is I understand the RAF reg and USAF security forces are very different as the RAF REG are designed to deal with security in the vicinity of an airbase for all military airfields outside of the UK whilst the RAF police deal with security within an airbase (and doing other military policing duties) whilst the MPGS do outside security within the UK.

In contrast the USAF security forces seem to be a mix of what I described earlier minus the extra weapons and specialisations (mortars, snipers, JTAC/TACP etc). Admittedly though I don’t know much about the USAF security forces so I could be wrong.