Unit Tests Vs System Tests

I've always know Unit Tests to be something you do in code. You write functions to test other functions. Our team has been working with the same project manager for a while now and he's always referring to system tests as unit tests. By system tests I mean the kinds of tests where a user follows a test plan and performs actions on an application to ensure it meets the requirements. This PM is an Indian offshore resource.

Is this use of terminology something unique to this person? Is it an Indian thing (like "do the needful")? Or am I just not aware that there's more than one definition for what a unit test is?