Both the 2013 and 2020 Pew surveys of American Jews contain four categories of respondents: Jews by religion (JBR), Jews of no religion (JNR), Persons of Jewish background (PJB), and Jewish affinity. The first two constitute the “NET Jewish population, meaning people counted as Jews. The fourth, “affinity” category consists of non-Jews who have an affinity for Jews. The third category consists of persons of Jewish parentage who (1) have a religion other than Judaism and consider themselves Jews and (2) have no religion and do not consider themselves Jewish. Persons of Jewish background (PJBs) are not considered Jews. The PJB population are in the Pew data sets but not in the report. They outnumber the JNR population. Using the 2013 and 2020 Pew surveys I show that on several attitudinal and behavioral measures PJBs are at least as “Jewish” as the JNRs. Since they are so similar, I question why are JNRs considered Jewish and PJBs are not. In light of this lack of distinction, I (1) revisit and adapt Sergio DellaPergola’s Jewish population classification system, (2) demonstrate that without considering DellaPergola’s “extended” Jewish population in our analyses we are missing important Jewish population dynamics, (3) examine the characteristics of the PJB population, and (4) propose some new screening questions designed for potential PJB respondents