There is not an official DSM diagnosis of "claustrophobia." Claustrophobia could be a Specific Phobia if the fear is something about the situation of being in an enclosed space (e.g., "I am afraid I will suffocate"). If the nature of the fear is that they are worried they will have a panic attack and not be able to escape, then Agoraphobia would likely be a more appropriate diagnosis.
so there's overlap between agoraphobia and claustrophobia?
There is not an official DSM diagnosis of "claustrophobia." Claustrophobia could be a Specific Phobia if the fear is something about the situation of being in an enclosed space (e.g., "I am afraid I will suffocate"). If the nature of the fear is that they are worried they will have a panic attack and not be able to escape, then Agoraphobia would likely be a more appropriate diagnosis.