Closed Primaries. In a closed primary, only voters registered with a given party can vote in that party's primary. States with closed primaries include party affiliation in voter registration so that the state has an official record of what party each voter is registered as.
Closed primaries preserve a party's freedom of association by better ensuring that only bona fide members of the party influence who that party nominates, but critics claim that closed primaries can exacerbate the radicalization that often occurs at the primary stage, when candidates must cater to their party's "base" rather than the political center.