You are. A .224 bullet, particularly a .224 softpoint or hollowpoint weighing 50-75 grains and travelling at 2000 feet per second or more, is a far cry from the 40-grain lead bullet of a .22 rimfire, particularly if it first penetrates window glass and pre-expands. The following profile is for a Remington 50-grain Jacketed softpoint bullet, as typically fired from a .223 or 5,56mm rifle.
The first is the older type:
The second is the newer type
You can see that both have similar wounding potential, while the newer type, being heavier, retains it's velocity and accurracy out to longer ranges, and also provides somewhat better penetration of intervening materials.