The line between the two is blurry, here's what might help you to conceptualize:
Sites are (mainly) about pages, while organizations are about user management.
If you have any pages, they are always part of a site. Trying to confuse you, an organization might have a site attached to it - and in that case there's a 1:1 relationship between the two. An organization is implicitly hierarchical, to the point that an Organization Administrator automatically gains administrative access on all suborganizations of the org that they are administrator in.
To confuse you further, sites might have members and can be hierarchical too. However, sites (I believe for historical reasons) have some self-service options optionally available: You can have open, restricted or private sites. Users can freely join or leave open sites. There's no such thing for Organizations - they're always considered to be centrally maintained.
With all of the changes, I agree that the distinction between the two gets more and more unclear (even though it's already clearer than in earlier releases when we had communities and organizations, with slightly other areas of responsibilities. So far, I believe that the "central vs self-service membership" conceptualization is the most helpful of the ones that I've seen.
Note that this is a simplified description - trying to make it easier to understand, not to be technically 100% complete. (it's meant to be correct but incomplete)
