RE: .45 Colt
No difference. The "official" name is .45 Colt, never been another.
Popular usage is a bit different. Some claim the "Long Colt" name came about when the US Army bought S&W Schofields in .45 S&W. It was dimensionally the same as the .45 Colt that was the standard service revolver cartridge, but was shorter. Thus the term "long", to designate the original Colt cartridge.
I've always used the term .45 Colt myself.