Sorry if this is a basic question, I didn't come up with a way to phrase a search to get any relevant results.

I am looking at replacing the crank on a 9 speed Trek 520. While I would ideally just buy a 9 speed branded crankset, I am curious if there is any reason one branded as an 8 or 10 speed wouldn't work. Is there an engineering difference between them that would cause me issues, or is more of marketing to sell groupsets as a whole?

The question has a second purpose as well, if an 8 speed crank with a 9 speed cassette is cool, the 9 speed cassette that is getting swapped out on the 520 for one with lower gearing is going on another bike.

doubt it matters much.. as at most the chain tip centers may be only slightly narrower... between each other
measure the width of the tip of the crankarm spider see if it brings the plane of the chainrings closer together.

When searching for an ideal crank length for my bad knees, I tried an old 2X5 cottered crank w/ 165mm arms for testing purposes on my 9 speed chain/cassette.
No issues.

Cool thanks all! Figured it wasn't a big deal, but I also couldn't figure out why they'd make such a big deal about it if it weren't.

separating money from the consumer.

Just remember that if you're changing gear ratios you will also have to change your chain length. I'm replacing my crank set which is set up 3X8 to one that is currently on a 3X6 bike. I want the taller crank gears on the 3X6 bike. Since both bikes will still need to be ridden, I'm using some chain from the one and splicing it into the shorter chain so I don't have to put new chain on used gears. If my basic math is correct, I should end up with two proper length chains and two rideable bikes. One with super low gearing and one with super tall gears.

Yeah, its getting a new cassette and chain too, I'll run it big-big plus two links sizing.

That should be long enough, but always (gently) verify.