The SD is the security department, they protect the facility until MTF arrive to assist in recontaining the SCPs. The security department is a no jokes department like the MTF. A picture:

The MTF is the team of soldiers that enter the facility to assist in recontainment protocols, they are the best of the best, no jokes soldiers. Made to combat riots and defectors. (explained in the next section.) the main ones are: NU-7, Alpha-1 Epsilon-11 and Beta-7.
Two pictures of the MTF:

The CI are defectors of the foundation, they fight to breach SCPs and free Class-Ds. Is the CI the Good ones? Loads of defectors joined the CI to free the Class-Ds. Other teams are on their side like Gru-P and the Serpents Hand.
A picture of the CI:

The GOC is a team that is allied with the foundation, they want to destroy the SCPs, I think thats why the SCPF contains them. Not much is known about them.

A team made to deal with anything, The RRT is the best of all of the roles. (except the 05 council and administration.) they mainly fight CI and Riots, When CI soldiers see The RRT they should run.

CI= Chaos Insurgency MTF= Mobile Task Force GOC= Global Occult Coalition RRT= Rapid Response Team SD= Security Department