What he said.
But yes, I figured Starfleet Security was supposed to be pretty badass. Tasha Yarr says their training is the best in the galaxy. It's just they're usually facing down things which can't be defeated physically.
While this is mostly Roddenberry, also, I could see an in-universe attempt to remove Starfleet's military connotations. Part of the nature of exploration and diplomacy as Starfleet's chief thing would include reassuring people they're not being invaded. Stating they're just "security" and not marines might actually be a bit of political senstitivity.