They BOTH measure the level of T4 in your blood, but take a different approach to it.
The Total T4 test (aka Thyroxine or simply T4) measures the TOTAL amount of T4 in your blood, including the T4 that is bound to proteins in your blood and not immediately available for your tissues to use. IF you have more binding proteins in your blood or less binding proteins in your blood than "normal", this test can be way off and not indicative of where your levels should be. It is, however, a less expensive test than the Free T4 as well as being an older test that doctors are more accustomed to ordering.
The Free T4 test (aka Free Thyroxine) measures only the T4 in your blood that is imediately available for your tissues to use (i.e. it is not bound to proteins). Several years ago, this test was not considered to be accurate, so many doctors decided then not to use it. These days, it is a very accurate test. Since it is more expensive than a Total T4 test, it is still often overlooked.
Despite the slightly higher cost, I prefer the Free T4 test any day. Actually, I prefer to measure Free T4 and Free T3 as well--fortunately, my doctor agrees. The same things apply to the Free T3 (aka Free Tri-iodothyronine) vs the Total T3 tests.
I am not a doctor, nor have I ever played one on TV...