"Claw toe" sounds like a figure of speech. The American Academy of Orthopaedic Surgeons uses it as a literal description, and its wording is specific.
The definition
The American Academy of Orthopaedic Surgeons says: "Having claw toe means your toes "claw," or curl, digging down into the soles of your shoes and creating painful calluses."
The joints named
The same source is exact about where the bend occurs: "In claw toe, the affected toe is bent at the middle joint, which is called the proximal interphalangeal (PIP) joint, and at the last joint, which is called the distal interphalangeal joint (DIP)."
The definition names two joints, not one.
Where the calluses and the shoes come in
The deformity is covered in the Royal National Orthopaedic Hospital patient guide to bunions and lesser toe deformities. The calluses named in the definition have their own page at APMA on corns and calluses, and the AAOS covers footwear in its OrthoInfo article on tight shoes and foot problems.
What to confirm, and with whom
If a toe curls the way the definition describes, have a foot doctor near Itasca look at it. Ask which toe joints are involved and what the calluses are telling them.
The clause readers skip
The definition ends on "painful calluses." The shape of the toe is one thing, and what it does to the sole of the shoe is the other.