Open primaries allow voters to vote in the primaries of any party, while closed primaries only allow them to vote in the primaries with which they are affiliated. Both types of primaries are held in the United States.
In addition to open and closed primaries, there are also semi-closed and top two primaries. The semi-closed primary allows voters that have no affiliations to choose which party to vote for, while voters with affiliations to a party may only vote in that party's primary. In the top two party, all candidates are put on the same ballot, no matter their party affiliation. It is primarily used in California, Washington and Nebraska.