Hip resurfacing is NOT where the orthopod goes into your hip and smoothes everything out, as the name might suggest. BHR is actually a metal-on-metal (MOM) hip prosthesis. It comprises a metal acetabular cup and a metal femoral head cap. The metal used is chromium cobolt nickel. THR's to date can be composed of metal and plastic, ceramic and ceramic, and the newer ones are large-head MOM. The biggest difference between a BHR and THR is in the femoral component of the prosthesis. In a THR, the head of the femur is amputated and a metal rod/spike is inserted into the femur which has a ball on the end acting as your new femoral head. In BHR, the femoral head is maintained, it is only reamed down ready for a metal cap to be firmly inserted over the top of the head.
Just for comparison here's a great image from the Mayo Clinic (http://www.mayoclinic.com/health/medical/IM03868):
BHR is therefore more bone conserving and is proving more beneficial to younger people with hip disease as it has allowed many to go back to more higher impact sports and activities compared to a traditional THR. However, it should be noted that the newer MOM THR's are allowing all ages to do exactly the same. The survival rates of BHR prosthesis have shown to be significantly higher than traditional THR at 10 years. But THR surgery has been around a lot longer than BHR (~15 yrs for BHR in UK; only since 2006 in the US), plus there is a skew in the age groups recieving either. So far the data falls in favour with BHR for younger people, but only time will tell.
I don't want to get bogged down with the pro's and con's here, I merely wanted to describe the main anatomical differences between BHR and THR.