"the only thing I can conclude with certainty is that if it says laminated, it's not one solid piece of wood"
That is correct - and it might not even be wood in any form. I have bought several very cheap soprano ukes from the AliExpress site. They are surprisingly good, if you just want a sturdy, OK sounding instrument. I keep one in my car.
I broke one up, in order to use its components for a hobby project, and was amazed at how strong was the sheet material from which the body was made. It appeared to be a synthetic laminate product. There was a core of coarse fibres, and they might have been of plant origin, but didn't really look like wood - as we know it, Jim! The outer surface has a very convincing wooden appearance and texture, but that seems to be printed.
'Formica' is the closest material to what I am attempting to describe. That was originally made using paper, I believe. Paper is itself a wood product, of course.
Anyway, whatever this stuff is, it makes very decent, cheap ukes, and should be much stronger and more tolerant of varying ambient conditions than is solid wood,or even laminated wood.
John Colter