Open primary
1. Partisan primary election in which the voter may choose a political party at the time of voting and vote in party-specific contests associated with that party, along with non-party-specific contests presented at the same election. Some states require voters to publicly declare their choice of party at the polling place, after which the election worker provides or activates the appropriate ballot. Other states allow the voters to make their choice of party within the privacy of the voting booth.
Source: Election Terminology Glossary - Draft, National Institute of Standards and Technology (NIST), https://pages.nist.gov/ElectionGlossary/
2. Primary election in which any voters can participate, regardless of their political affiliation. Some states require voters to publicly declare their choice of party ballot at the polling place, after which the poll worker provides or activates the appropriate ballot. Other states allow the voters to make their choice of party ballot within the privacy of the voting booth.
Source: Glossary of terms database, U.S. Election Assistance Commission, https://www.eac.gov/glossary/