You ask a very good question. Perhaps only a surgeon can really appreciate the difference between the two operations. A total hip replacement is invasive no matter how it's done. A better way to look at it is to say it "minimizes the invasiveness". From a patient's point of view, it certainly does sound invasive.
The first difference and reason why it's called "minimally invasive" (MI) is the length of the scar. MI means the incision is about two inches long. A full incision can be up to eight or 10 inches long.
During the operation fewer muscles are cut. New tools allow the surgeon to gently move structures out of the way to get to the hip. Anything that is cut is carefully repaired and put back in place.
More and more surgeons are getting trained in this new technique. We can expect it to improve even more over the next few years.