"Marines", "soldiers" or "Army" all carry the connotation that this is an organization somehow separate from "Starfleet proper". There's no evidence of there existing any
organizations separate from Starfleet proper, though: things like Starfleet Security and Starfleet Medical all appear to be part of the same organization, with parallel branches in a hierarchy consisting of many more or less identical branches.
We have seen people we could interpret as being ground fighting specialists. But we have also seen engineering specialists, medical specialists and people specializing in astrophysics. They all carry the same Starfleet-pattern (that is, Navy-pattern) ranks and answer to the same generic Starfleet bosses, even if through a department head who's also something of a specialist (but most of the explicit department heads we see are actually generalists!).
Moreover, when we do see ground fighters, they, too, have Starfleet-pattern ranks: the people who fought at AR-558 were commanded by a Captain and then a Commander, supposedly in that order, not by a Colonel and a Major. The remaining evidence is neutral, with the rank of Lieutenant assigned to a ground fighter or three, making it impossible to distinguish between Navy and Army patterns. There has never been a Starfleet officer or crewman performing ground fighting duties and carrying an Army-pattern rank.
None of this means there wouldn't exist a specialist branch in Starfleet dedicated to ground fighting, or boarding action, or aerial fighting or whatnot; perhaps there even exist separate branches for all, with some people dedicating their careers to mastering the art of fighting in an antigrav harness a minimum of fifty meters off the ground, and others serving in a specialist force that fights on the outer hulls of starships. Perhaps the existence of multiple small branches like that is what preempts the use of the term "Marines" in Star Trek dialogue?