Note that "freighter" is an explicitly civilian term because it charges freight - that is, it charges money or a fee for conveying its cargo. In fact in the age of sail warships could often charge freight money, because they would be used to convey high value articles like bullion, with the captain (and admiral) receiving a small percentage of the total value.
The generic term for things that haul stuff is usually a cargo ship or carrier. Transports, tenders, tankers, colliers, ammunition ships, all fall under those distinctions as auxiliaries.
I do tend to wonder at what level Starfleet maintains auxiliaries and whether or not they repurpose starships for that purpose. The extensive starbase network would seem to argue against them having a large fleet of auxiliaries, if only because the starbases seem to be pretty self-sufficient.