I'm with you Deja Vu, but I'll add that generally if the animal had a different number of points on one side then we'll count both. For instance, a 3x4 would be a buck with 3 points on one side and 4 on the other. It is also acceptable to refer to, say, a "4-point" mule deer buck as a 4x4 OR a 4-point. This is especially true with elk, most often you'll hear both sides even if both sides are the same.
We DO NOT include eye guard tines for deer! A 4x4 mulie with or without eyeguards is still a 4-point. Same goes with our subspecies of whitetail, the Coues whitetail. A 10-point whitetail buck in Alabama would be a 4x4 whitetail in AZ. If the eyeguards are worth a mention, say one side had double tines on the eyeguard... that would be a 4x4 with a double eyeguard and NOT an 11-point
Elk don't have eyeguards so generally all major points are counted. Small tits that stick off main points are often times not counted either, especially on elk.
I think it'd be easier to just count all the damn points! But is still sounds goofy (to me and my western lingo) to go around saying "I killed a 12-point buck."