This has been what's in my house/apartments since I was 8 and first learned about them when ours went out and my grandpa came over to fix it.
Heat pump, with 1-3 rows of coils for electric backup heat. Lowest Temps I've experienced were -20F and highest were 110F. Struggled to cool below 75 at the top, and heat above 60 at the lows. But those are rare extremes (on the low side anyway, I expect the high side to "peak" more often in coming years)