From looking at the outside- you normally wouldn't see a difference, but there is actually a very big difference. While an air conditioners only function is to cool your home, a heat pump cools your home BUT it also heats your home. That's what makes the heat pump so much more energy efficient.
When you switch your thermostat to heat, the refrigerant in the system reverses direction and creates heat. Systems in our area generally produce heat until the outdoor temperature reaches 30 degrees. Once that happens, your system will automatically bring on the back up heat (emergency or auxiliary heat)- which can be gas, electric, geothermal, oil, or whatever type of indoor system you have. You can imagine how costly it can be some winter months if the back up is electric.
Higher than normal electric bills, in any season. is a good indication to have your heat pump checked for normal operations. We-along with most major equipment manufacturers and the EPA- actually recommend to be done seasonally.
If you aren't familiar with a heat pump, the sight of it at times in the winter may cause you concern. These systems will get a heavy layer of frost on them when heating in the winter, this is normal as long as the system defrosts. The defrost cycle can often cause concern due to hissing noise and steam (which is often mistaken for smoke) but is a normal function of the heat pump. If the frost keeps building up, this is an indication of an issue, and you should call for service.
Heat pumps are designed for energy efficiency, but to maintain energy efficiency the system must be operating normally, and unless you spend lots of time outdoors in the winter, its not always easy to know if you are having an issue because your home will often still be warm and comfy thanks to the backup heat source. Another great reason to have seasonal maintenance.
If your system is older, or having more and more service issues and you're considering replacement, you might want to consider the heat pump as an option now that you have (hopefully) a basic understanding of a heat pump.