"Marines", "soldiers" or "Army" all carry the connotation that this is an organization somehow separate from "Starfleet proper".
Not necessarily. Starfleet Marines would still be considered Starfleet officers. They just have a different specialty, that's all. They would attend the same Academy as the rest of Starfleet (just like US Marine officers are graduates of the Naval Academy). They'll just have different ranks, like Major, Colonel, General, etc. Doesn't make them any less Starfleet.