Despite the issue that the version of the "Operation Retrieve" chart used as evidence for the "Starfleet Marines" may actually be incorrect (more recent photos of the actual prop show the notion 'Effective Limit of Surface Containment Force Field' rather than 'Standby Ground Troops Starfleet Tactical Marine Corps Entry Point') there is a certain logic within limits to the 'error'.
Starfleet Tactical was introduced in dialogue as a unit/branch in Best of Both Worlds, this established that they were tasked with military R & D and in peach time with co-ordinating military/defense operations (or advising Starfleet Operations on same). Therefore it's not much of a stretch that they would have been involving in "Operation Retrieve". [NB it is possible indeed probable that they are descended from the TrekLit's Defense Service (Andorian Guard)]
We know that there is a Tactical Analysis Division (Shelby was likely assigned here prior to BoBW), so it reasonable to assume that they also have a number of field units, potentially including something called a "Marine Corps".
So I would suggest that the STMC is a corps (or potentially demi-division ala the Royal Marine Commandos)-sized rapid reaction/special operations force specifically tailored to polar/mountain warfare and referred to as the 'Marine Corps' because while army units can specialise in either desert warfare (as the similar unit from TFF likely did) or polar/mountain warfare, marines (especially the Royal Marine Commandos and the Dutch Korps Mariniers) tend to prioritise the latter, though most are certainly capable of engaging in desert warfare rather than a general purpose 'ship's security and boarding team' which IMO is better suited to HRT-style units drawn from Starfleet Security (cf USAF Security Forces with elements of RAF Regiment).
Starfleet Tactical was introduced in dialogue as a unit/branch in Best of Both Worlds, this established that they were tasked with military R & D and in peach time with co-ordinating military/defense operations (or advising Starfleet Operations on same). Therefore it's not much of a stretch that they would have been involving in "Operation Retrieve". [NB it is possible indeed probable that they are descended from the TrekLit's Defense Service (Andorian Guard)]
We know that there is a Tactical Analysis Division (Shelby was likely assigned here prior to BoBW), so it reasonable to assume that they also have a number of field units, potentially including something called a "Marine Corps".
So I would suggest that the STMC is a corps (or potentially demi-division ala the Royal Marine Commandos)-sized rapid reaction/special operations force specifically tailored to polar/mountain warfare and referred to as the 'Marine Corps' because while army units can specialise in either desert warfare (as the similar unit from TFF likely did) or polar/mountain warfare, marines (especially the Royal Marine Commandos and the Dutch Korps Mariniers) tend to prioritise the latter, though most are certainly capable of engaging in desert warfare rather than a general purpose 'ship's security and boarding team' which IMO is better suited to HRT-style units drawn from Starfleet Security (cf USAF Security Forces with elements of RAF Regiment).