Those are most definately bites, and to be expected if there are 2 of these fish in the same tank. The only way to prevent losing one of those fish is to get them seperated asap! Fahaka puffers are known to be extremely aggressive, especially with their own kind. These are great fish if you want a really large tank (125 gallons or more) and 1 large fish (they grow to 18 inches).
There is possibly the starts of a fungal infection on at least one of those bites, based on the photos. Methylene blue is safe to use and should help prevent further infection from setting in while it heals. Remember, if the 2 fish stay together, this is only going to get worse until the fish dies. They simply can't be kept with anything else.