One difference between squirrels (which I shot a whole lot of before moving to Alaska) and rabbits of all varieties is "pose." How they are positioned when they stop.
I bet more than half the squirrels I shot were laid out flat rather than upright. But every rabbit I've ever shot while it was sitting still was upright, with it's forelegs down over it's body. Side shots to the body are going to connect with forelegs, and frontal shots are going to take spine.
I did about 90% of my squirrel hunting with a handgun, either a K-38 or K-22, and my only concern in hitting squirrels was the front half of the body, including head. If I could see any of that, it was often a dead squirrel with no real concern for meat loss. Using handguns today for snowshoe hares, it's still a headshot-only deal.