So, there is no distinction between the two because they both enjoy doing it?
Hunting for the purpose of food acknowledges that the animal's life has value. Yes, these hunters enjoy what they do, but they respect the animal enough to make sure it's life was not taken frivolously. The person buying their meat at the store (yes, that's me) doesn't know where it came from or how it was raised. The hunter knows that the animal lived freely the way it was intended. There is a certain ethic here that I respect.
The sport hunter does it purely for vanity and has no respect for the animal. They take their trophy and leave the carcass behind. Taking a life should carry some moral weight. Something these guys clearly lack.