Identity testing asks “is this the compound it is claimed to be?” — typically confirmed by comparing an observed molecular mass against the theoretical mass calculated from the compound’s known sequence or structure. Purity testing asks a different question: “of everything detected in this sample, what proportion is the intended compound?” A sample can have confirmed identity and still carry impurities — related substances, byproducts of synthesis, or residual solvents — that a purity test quantifies.
A reference standard is a well-characterized sample of a compound, used to calibrate an analytical method and confirm it is measuring correctly — a known quantity a lab compares an unknown sample against.
“Purity” and “identity” being different measurements is also why they are reported separately on a certificate of analysis rather than collapsed into a single figure.