I think that fits the on-screen evidence best. Starfleet's shipboard security teams seem a good match for the early incarnations of US or British Marines. Just as the US Navy began combining shipboard detachments into a larger Fleet Marine Force, which in turn evolved into something bigger and much more extensive, I can see Starfleet's shipboard security being the initial basis of something that became (or could become, if needed) a larger and semi-independent "ground" force.
Possible, even plausible, but I doubt Roddenberry ever thought that out.
As for terminology, as an all-rolled-into-one "combined service" Starfleet may intentionally avoid terms traditionally tied to one environment like "army," "navy" or "marines." The titles of ranks don't really mean much in the long run; while Britain and the US put army-type units aboard ship as marines, other nations worked the other way and organized sailors into marine/naval infantry forces with naval-style titles, insignia and dress uniforms. And for 70 years the US Navy has had Seabee units with naval-type ranks running land-type units -- regiments, battalions companies and so on -- and it has worked fine.
True, but Roddenberry deliberately chose to use the structure and ranks of the US Navy as it existed then to connect to the audience more easily. When TMP was made, their research company advised them to make Kirk an admiral,not a commodore, because the US Navy had changed the rank between TOS and TMP, and they went with it because they were still tied to following their real-world model. Now, by TNG, they no longer used a research company (it was a department of Desilu during TOS, and during TMP, movie companies still contracted that service, but by now it's mostly just a search service to avoid using copyrighted or real-world names without permission), and stopped trying to match things up to the real world, but if Roddenberry had intended
the "combined service" thing to cover this, I think he'd have included some dialog to that effect and shown somewhere some naval infantry or other service types rolled under the Starfleet umbrella.