Right, that's my understanding as well. There's actually _many_ different unemployment numbers, depending on what definition of employment vs not vs not even included that you want to use. The "unemployment number" without qualification we tend to use is (IMO) kind of crap, but we're stuck with it for tradition mostly as far as I can tell.

https://www.bls.gov/news.release/empsit.t15.htm seems to be the best resource I can find at the moment for the ones I'm thinking of, it doesn't really define them very exactly though. I'm sure they're defined _somewhere_.