What is a caucus, and what is a primary?

A caucus and a primary are the two most used methods for US political parties to nominate candidates to put on the ballot for the general election.
A caucus generally happens at the local or precinct level. Members of the political party who live in the area gather to discuss issues and vote on which candidate they support for the nomination. In some states, the votes are tallied from all local or precinct caucuses, and the winner gains the nomination (or, at the presidential level, determines the percentage of the state's delegates to the national convention are committed to support each candidate). In other states, the local caucus selects a representative to go on to a county convention to support the candidate the caucus selects. From the county convention, a representative is selected to support a candidate at a statewide convention, which, at the presidential level, then allocates delegates to the national convention.
A primary, on the other hand, is run by the state similarly to a general election, except that only members of the political party are eligible to vote on that party's ballot—with some exceptions. The winner of the primary is that party's nominee for the general election ballot. Some of the exceptions include the following:
A political party can choose to allow crossover voting, which means members of other political parties and/or independent/unaffiliated voters can cast ballots in the primary.
A jungle primary throws all candidates onto the ballot. If one candidate gets at least 50% of the vote plus one, they win the election. If no candidate receives a majority of the votes, then the top two candidates advance to the general election or a runoff election. Some states allow candidates of the same party to advance to the runoff, so you could have two Democrats on the general election ballot. Other states take the top candidate from each of the two major parties to the general election.
https://uselections.com/QandA/primary-caucus-convention.shtml

https://www.diffen.com/difference/Caucus_vs_Primary