How does vinegar get rust off these coins
As previous comments said, this isn't a redox reaction.

The patina or corrosion is made of metal salts -- for copper, it's copper oxide, sulfide, carbonate, and perhaps other things. Vinegar readily converts all these to soluble copper acetate.

Most coins are made of metal alloys, and those alloys sometimes contain metals that are attacked by acid. Nickel and zinc are common components. Soaking in vinegar will dissolve these metals (they'll displace hydrogen, again forming soluble metal acetates). This damages the coin's surface, making it porous, and eventually reducing the coin's weight. (It also breaks collectors' hearts.)

Adding salt to the mix forms an equilibrium with hydrochloric acid, which attacks metals even more aggressively. Please don't do this unless you don't mind ruining your coins.