It's a matter of degree. Go do some research.
When people talk about "corrosive" ammo, they are primarily talking about primers that are made form mercury-based compounds. These leave corrosive slats in the bore that if not flushed out with hot, soapy water will lead to rusting very quickly. 1950's and earlier ammo was almost (note the almost) all corrosive. Some countries still produce corrosive primers.
Blackpowder acted in a very similar manner.
Today with modern primers and smokeless powders, shooting your firearm and not cleaning it right away is not a death knell for rust. Left unattended, ANY metal will eventually corrode.