a trimmer to me has always implied multi-turn precision adjustable.
I think the "real" difference is in the number of times that you are supposed to change te setting. A "trimpot" is something that you're supposed to adjust "few" time, and then leave there, while a pot used as a volume control (for example) should be designed to be turned up an down thousands of times. (somewhere in the datasheets area specs for such things...)