Define a primary, a caucus and a general election. What are the different types of primaries

Define a primary, a caucus and a general election. What are the different types of primaries; include in your answer for each specifics about who is eligible to vote, the ballots, and the impact of crossing over at the presidential level, including how ballots are designated when crossing over is a factor. Why might the Republican and Democratic parties prefer the caucus over any of the primary options?