What is the difference between an AC Cobra and a Shelby Cobra?

I think that the AC Cobra was made first then Shelby made them with bigger more powerful motor.

The Cobra was Shelby's creation and was badged as a Shelby in North America. In Britain they built some as AC. They were the same car, although I can't be sure that some small differences in spec resulted.

Lizard:

I believe you're almost spot on. The AC Cobra and Shelby Cobra were the same (I believe EXACTLY the same) cars. AC Cars marketed the car in England under their badge and Shelby marketed the car in the US under his name.

The car was the AC Ace before Shelby put the bigger engine in it.