Matt is correct-to a point. .45 auto+.45 ACP are the same-BUT- There is, in semi-auto: .45 Auto Rim .45Gap .45 Magnum. Revolver ctg-45 Colt, is also popular to the Cowboy Action group. In general when someone says I have a .45Auto, they mean .45ACP

Well then, let's not forget .45 Long Colt, .45 Super, .45 Remington-Thompson, .45 Winchester Magnum, or .45 Peters.
.45 Auto is a synonym for .45 Auto Colt Pistol. Always has been, always will be. C.I.P., and because of it, the rest of the world knows the .45 ACP as .45 Auto. C.I.P. is the authority in ammo worldwide. SAAMI is only king in the US.
CIP lists the maximum pressure allowable by a .45 Auto at 18,885 PSI, whereas, SAAMI allows for 21 kPSI. Other than that, the 2 are identical.