Is fat grafting the same as fat transfer?

Fat grafting and fat transfer are the same. Taking fat from one part of the body, processing it and injecting it somewhere else is done to help reverse the "deflation" we suffer as we age, lose facial fat, collagen, and skin thickness. Fat grafting is usually done for the face, but is also used in other areas such as the hands where age can create unwanted changes. Fat transfer is often a better alternative than fillers if there is a large amount of volume needed. Fat tends to last longer than most fillers.
The fat is often taken from the outer thigh, so a person who has essentially no body fat would not be a good candidate for fat transfer. Fat transfer is often a good adjunct to a facelift done at the same time so that the sagging skin can be lifted, and the missing volume replaced.

Yes, fat transfer and fat grafting are different terms for the same procedure. For this procedure, fat is typically taken from the abdomen or thighs and injected into the face as opposed to traditional soft tissue fillers.