I think you've already answered your own question.
Two point means you have two points of contact with the saddle, meaning your knees - your buttocks and crotch are out of the saddle, and you are folded forward at the hip. Three point is with your crotch as the third point of contact, buttocks still out of the saddle and the rider folding forward at the hip.
Some instructors teach beginning jumping by having the riders *approach* and land from the jump in two point, others teach to ride to the jump posting the trot or sitting the canter and allow the motion of the horse to push the rider out of the saddle.
The position in the air over the fence should almost always be two point, or at least, that's my opinion. But I don't know everything like the lady at your barn does.