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This article from 2013 outlines the differences quite nicely. It's a subtle point (that I hadn't appreciated before reading the article), but trim on a Cessna (on which many pilots learn) and modern jet work quite differently, though you rarely ever notice the difference in normal ops (because you never go massively out of trim). The author speculates that several accidents might be attributable to this.

Do you really understand how your trim works? Many do not, and why it matters. Alex Fisher - GAPAN

https://www.skybrary.aero/bookshelf/books/2627.pdf

I only really appreciated this while reading while reading about https://en.wikipedia.org/wiki/Alaska_Airlines_Flight_261

It's quite an interesting one if you are into that kind of thing.

Well an MD-80 does use trim tabs.

Not really. It trims via a moving stabiliser. You are confused because it has flying elevators and the pilot only directly controls the servo tabs which look a lot like trim tabs.

Ah yes, brain fart. Tabs for the elevator, jackscrew for the stabilizer.

Ah ok, that make sense.