Strictly speaking, Starfleet doesn't operate a standing military organization, so their combat training is just one aspect of a VERY extensive curriculum.
Starfleet IS a standing military organization.
From TOS to "The Undiscovered Country" it would appear that this is true to a certain extent.
Kirk and some of the crew are multi-role soldiers who happen to explore and perform diplomatic duties during peace time. Others like Jaeger from "The Squire of Gothos" are dedicated scientists who go along for the ride.
"Errand of Mercy"
KIRK: That's the first thing that would be lost! Excuse me, gentlemen. I'm a soldier, not a diplomat. I can only tell you the truth.
"Metamorphosis"
KIRK: I'm in command, Bones. It makes it my fault. How do you fight a thing like that?
MCCOY: Maybe you're a soldier so often that you forget you're also trained to be a diplomat. Why not try a carrot instead of a stick?
"Whom Gods Destroy"
GARTH: Upon the firmest of foundations, Mister Spock. Enlightened self interest. You, Captain, are second only to me as the finest military commander in the galaxy.
KIRK: That's very flattering. I am primarily an explorer now, Captain Garth.
GARTH: And so have I been. I have charted more new worlds than any man in history.
"The Wrath of Khan"
MADISON: It seems clear that Starfleet never intended that.
CAROL: I know that, but...
DAVID: I've tried to tell you before. Scientists have always been pawns of the military.
CAROL: Starfleet has kept the peace for a hundred years. I cannot and will not subscribe to your interpretation of this event.
"The Undiscovered Country"
SPOCK: The dismantling of our space stations and starbases along the Neutral Zone, an end to almost seventy years of unremitting hostility with the Klingons, which the Klingons can no longer afford.
MILITARY AIDE: Bill, are we talking about mothballing the Starfleet?
C in C: I'm sure that our exploration and scientific programs would be unaffected, Captain, but...
So we can guess that after ST6 there was a reduction in Starfleet's military program which lead to the more peace-oriented explorers of TNG and later.