They seemed to wear uniforms and insignia. And the badges were similar to what Gillian Taylor wore at the end of STIV.Lorca gave Stamets a verbal smackdown once or twice also. Stamets in fairness, didn't seem to understand what he was buying into when he accepted an officer's commission in exchange for getting his project funded. He should have held off for a sweet non-uniform gig like Carol Marcus an Son got.
I would propose that Carol's team were members of a Federation uniformed service that exists alongside Starfleet. It would put the soldier vs scientist references in TWOK into the context of interagency rivalry.