That seems really weird, the only real difference is a reversing valve that costs a couple bucks. A heat pump is an AC, it just can be run backwards to produce heating as well. In cooling it's literally the same thing.
I'm no expert but the difference in the real world is more than that (though am doubtful about 3x the price) . The delta-T between heating and cooling is significantly greater in most places so you need a bigger system. You also need things like the ability to de-ice.