To give a slightly more technical answer, at a large insurance company I used to work for, the legal department had provided definitions on what conditions we would consider various components of PII a match. So between SSN, DoB, First Name, Last Name, and a couple others, there were potential combinations that our system would say, "yes this is the same person". Note that we didn't necessarily need exact matches on things like names, but "close enough" matches were sometimes sufficient.