trail rig = almost any stock to mildly built rig. Good road manners and does "so-so" off road.
mud bogger = big tires, & lots of HP. High center of gravity. Not good for much else. Poor road manners.
sand dragger = small tires but not streetable. Low center of gravity. Lots of Hp. Usually single purpose & not a trail rig.
rock crawler = depends on definition. 37-40" tires. Great trail rigs, will handle almost any terrain. so-so on the road.
road driver = good on mild offroad experiences but not good for anything above mild.
If you are looking to get involved in offroading but don't know what you really want to do, put a set of 33 - 35" tires on any 'ol rig and start getting involved.
One other point, in today's world, trespassing and tearing shit up just to have fun is frowned on and hurts the entire sport. just something to keep in mind...................