"...often a lot of overlap between a System Test and and Acceptance Test."

The way I see it, an acceptance test can test just part of the system (e.g. all input facilities, a certain interface, etc...), but is always performed by, or at least verified by, the end user.

A system test should include all parts of the system, not just one or more sub-systems.
As you stated, it's performed to find out whether the system behaves as a whole.

Cheers,
MichaelD