Timo says:
That is, there would be Military Assault Command for ground fighting (that's what "military" has meant for most of the time the word has existed - the opposite of "naval"), and possibly parallel Military Logistics Command, Military Communications Command and so forth. Or subsections like Military Assault Command (Ops), Military Assault Command (Logistics) etc.
I'd combine your suggestions. Only a fraction of the military is actually involved in assaults, and of those, only a portion are the actual operators. A partial, speculative order of battle might look something like this:
Civilian Government
-Starfleet Command
-Maritime Patrol Command
-Military Command
--Military Assault Command
---MAC Operations (MACOs) -- carry guns, take and hold things.
---MAC Logistics -- provides beans and bullets for MACOs when operating apart from Starfleet.
---MAC Miscellaneous -- personnel, training, intel, etc.
--Military Stability and Support Command
---MSASC Operations -- foreign internal defense, low-intensity conflict
---MSASC Logistics -- feeds and arms the MSASCOs
---MSASC Miscellaneous
--Military Support Command
---MSC Operations -- MC-wide planning and operations
---MSC Training -- MC-wide training
And so forth and so on. In my fanboyish order of battle, the Military Command is generally responsible for "boots on the ground/deck" force, except when the prima donnas in Starfleet insist that their own "security" personnel are sufficient for such things. The MAC is the MC unit responsible for killing people and breaking stuff, and the MACOs are the tip of that particular spear.
By Kirk's time, the MC was placed under SF in the org chart, so the commander of the Military Command always reports to the top guy (or gal) in Starfleet. By TUC they're even wearing Starfleet uniforms. But their ranks, and maybe even their organization, could have remained intact from the United Earth days.
I'm also completely open to the idea that Colonel is a given name. Can't be sure until we get some canonical clarification on that point.