Yes, physiologically they are same for USMLE purposes. Also, I did an endocrine rotation when I was in med school, and clinically it's considered the same.
PTH-rP is just high in bronchogenic squamous (usually the example they like), as you know. If it's high, then endogenous PTH must be low to compensate (if they give you an arrow question).
They have a different structure . PTHrp is just a 34 AA part of the whole PTH molecule , which gives it functionality. Plus , PTHrp will not be detected by assays used for PTH