I have enjoyed this thread, I must say! Where I live, trawlers are commercial fishing boats that trawl nets compared to similar dimension boats that might also be full displacement, single engine, wood construction, but which fish pole and line. Both are called "fishing boats" but only one of them is a trawler. Both have fish wells, but only the latter has live bait tanks. These kinds of fishing boats have huge carrying capacities; for example, one of the other fishing boats here displaces 12 tons and can carry 10. Most go out in all but the worst conditions and stay out days at a time.
I know you all know this—I make this point only to highlight the extent to which the recreational boat building community has taken the attributes of seaworthiness that these vessels have to have and labelled a number of vessels they sell as "trawlers", but they do not appear to share many of the characteristics of fishing boats. How could they? They are designed with very different goals in mind.
My new boat is labeled a trawler by its designer, and no doubt shares some DNA with the wooden boats I described. In reality, it is a full-displacement, single engine, carvel construction wooden boat that has the sheer lines of some of the fishing boats in this area, but has been designed as a live-aboard boat (so different engine placement, for example, not needing a fish well).
Here in Australia, as far as I know, "yacht" describes two kinds of boats: those with sails and much larger pleasure boats. I think we borrowed the American usage for the pleasure boats.