The 45 Auto Rim cartridge has been around since 1920 or so, and the moon clips for the 45 ACP have been around since WW1 when revolvers were being retrofitted to fire the 45 ACP to keep the sidearm ammo consistent with the Colt 1911s. This keptlogistics easier during the war. The 45 Auto Rim was designed to eliminate the need for the moon clips later on.

For deer hunting, the 44 mag will be fine. Keep it within 100 yards for terminal performance when conditions are perfect, and reduce the range depending on angle, lighting, and personal proficiency. I won't shoot past where my groups get to be 6" big. Some states have minimum muzzle energies listed for deer hunting handgun cartridges, and others may list specific calibers. Some states also forbid semiautos for deer hunting.

I carry the S&W 629 -6 incher as a backup to the shotgun during firearm deer seasons. I wear it crossdraw so I can shoot to mystrong side in case I can't swing the long gun around while sitting or standingup against a tree. When using it as a primary game-taking device, I'll throw a red dot or 2x scopeon top and tuck it in a bandolier style holster, but as a backup, the iron sights are fine for me. My front sight has a bright orange insert that will make easy work of surprise up-close shots where speed is a priority. When hunting in heavy cover, the deer can get right on top of you before you see them.