You can get an appliance that can do both, well and efficiently. Every modern AC has a reverting valve that changes the flow direction of liquid and gas, such that the liquifier and gasifier change places. For cooling, the liquifier is in the outdoor unit, for heating it is in the indoor unit. Common refrigerants (for new units, the choice is R32 or R290) have a temperature range that works for both functions. Depending on the refrigerant the efficiency will differ, but in both cases it will be above 250% to 350%. Meaning for every kWh of electricity, you get at least 2.5 to 3.5 kWh of heating. Or cooling.
The easiest and cheapest way to get such a device is to get an air-air AC unit. More than 90% do have a reverting valve and can heat and cool. All of them will be efficient in both functions. Just look at the SEER and COOP values or the A+/A++/A+++/A+++++++ ridiculousness/efficiency scales ;)
Those air-air heatpumps/AC units can do both because they basically have the same radiator on both sides, and the same condensation removal system. Sometimes the cooling is a little more efficient, sometimes the heating is. This basically depends on the refrigerant used and on the local climate you are using the unit in.
Condensate is the reason that at least in Germany, you sometimes cannot do both. The usual heatpump you buy around here is an air-water heatpump. Meaning the outdoor unit is coupled via outdoor air. The indoor unit distributes it's energy through water, usually in water radiators or in-floor heating. Problem with that is that those water radiators are not suited to be run with cold water for cooling, and those in-floor heating systems usually aren't as well. Why? Because water will condense on those cold surfaces during summer, run off into your flooring and cause rot there. If you paid attention to make your flooring condensate-proof or have even more cooling surfaces from in-wall or in-ceiling loops, you can also run cooling this way. But most people can't.
So yes, you could do both if you put in a single air-air heatpump / AC. In certain rare circumstances you might also do it with an air-water heatpump.
Oh, and there is the theoretical option to do air-air and air-water with the same single outdoor unit and multiple air-based indoor units and one or two water-based indoor units that create warm water for heating and piping. Look for multi-split systems. But for the usual small single-family homes, those aren't cost efficient. They are therefore usually only offered for commercial applications such as hotels. But they have nice advantages like using the heat produced from the AC to heat the water used for the showers and stuff.