There are two terms in the dog fancy that you won’t find in the AKC breed standards of the two breeds in which the terms are most often used: Shark Nose and Roman Nose.
And they are not the same thing.
Used colloquially in their respective breeds, “shark nose” refers to the nose in a Scottish Terrier that projects over the dog’s mouth and gives the impression that the dog’s upper jaw is longer than his or her lower jaw. It creates a pointy and slightly elongated profile which is at odds with the standard that calls for a muzzle that should be “approximately equal to the length of skull with only a slight taper to the nose.” It isn’t desirable in this breed.
A Roman Nose (also known as a “Ram’s Nose”) is used in other breeds, but it is most often associated with Bull Terriers and refers to a more rounded nose shape. Such a nose is characterized by a prominent, convex curve along the bridge of the nose giving the dog a distinctive, arched profile. In the Bull Terrier, it is the result of the bridge of the nose bending downward because of the convex curve of the bridge from the junction of the back skull with the fore face to the tip of the nose. The breed standard describes this desirable feature as a full face oval in outline, and “egg shaped.”
While these are slang terms, each aptly describe a nose shape that impacts the dog’s appearance, one desirable, the other not.
Image: Scottish Terrier* by eAlisa/Deposit; Bull Terrier by © Seregraff/Dreamstime. *Scottie’s nose profile has been manipulated to be more “shark-like. The original photo is seen here.