Hard drives can't run fast enough to justify using SATA III ports for speed, but they can use them for the extended capabilities (eg: NCQ). So some hard drives are marked as SATA III, and some aren't.
Even so, you can generally plug SATA II hard drives into SATA III ports without problems, and you can plug SATA III hard drives into SATA II ports without problems.
Most new motherboards have a mix of ports, some SATA III, some SATA II. If you have the option, then use the SATA II ports for your SATA II hard drive. The manual will tell you which is which.