See what each type of test describes. An acceptance test is tested if the system under test is acceptable to end users, that is, customers. This usually includes a general test to ensure that the program is acceptable. There may be some errors in sysyem (for example, some localization errors or a more serious error if the user does something unusual), but while this is not an obstacle to the general use of the program, the program may (think about Microsoft - if they took the time, to fix every mistake they and the clients came with, we will still be working with Windows 95).
A system test for comparison is a test of the system in which the program runs. Thus, the acceptance test may say that the program works fine on Windows 95; but if the program crashes when you try to run it on Windows 7, and most clients are running Windows 7, you need to change the system test.
This, of course, is a very general answer, but the key also lies in the fact that both tests should include testers and clients. Testing, which includes only a tester or developer (e.g. Unit Testing), is what WAY needs to do before you get to the acceptance or testing phase of the system.