Is this use of terminology something unique to this person?
I have no idea if this specific use of terminology is unique or not, but it is not uncommon to find teams or persons in the software industry using terms in a quite unusual, non-standard, or imprecise way.
For example, due to the popularity of tools like JUnit or NUnit, I have very often heard people using the term "unit test" for any kind of automated test driven by one of those tools, and not just for "unit tests" in the proper meaning of that term.
Such a sloppy terminology can be ok to some degree, as long as everyone in the team knows what is meant, and as long as one is aware that the rest of the world might use some some terms a little bit different.
However, using "unit test" as a synonym for "system tests" or forms of non-automated testnon-unit tests is something I have never heard before. For me, this usage sounds so utterly wrong that I would recommend to give your PM a hint that his/her usage of those terms bears a certain risk of producing misunderstandings.