How to explain on-prem vs. O365 vs. hosted (aws for example)

Is the description "on-prem" technically/strictly referring to when we have our own servers in-house? Or can that also apply for example when running a SP farm in a hosted VM? And I assume all that's different than O365 (which is I guess only referring to hosted by Microsoft).

These configuration definitions could be helpful when reading how-to articles online for example, especially if on-prem examples are actually applicable to hosted situations where you're still in control of some part of the setup/config.