Is there a difference between a calcium vs. Ionized calcium test?

Yes. Calcium has a positive electrical charge; many proteins have a negative electrical charge. So, the opposite charges can cause calcium can bind to proteins. The test for serum calcium measures all of the calcium in the blood (bound & unbound). The ionized calcium measures just the unbound.
Yes . A total calcium is dependent on your Albumin level, which is a blood protein to which calcium is bound. The ionized calcium is a measure of unbound calcium (physiologically available) & may be more accurate in terms of estimating available calcium. However, special handling of blood sample and difficulty performing this test in a lab makes it more expensive.