Are you familiar with U.S. elections? Caucuses are very much part of the primaries. They are how certain states perform their primaries. Iowa, for example.
Yes. Intimately.
> Caucuses are very much part of the primaries. They are how certain states perform their primaries.
No, caucuses are a (formerly, universally used—primaries are a newer thing) alternative to primaries still used in a minority of states (and sometimes, by some parties but not others in a state) to select delegates to Presidential nominating conventions.
Because primaries have over time displaced caucuses as the main candidate selection mechanism, and because the campaigns are somewhat nationalized, and because there isn't a handy name for the whole process, the whole national process of selecting such delegates is sometimes sloppily referred to as “the primary” of each party.
This is a disconnect on jargon. Primaries mean elections. Caucuses are an alternative to primaries. Both primaries and elections constitute the process by which American parties select delegates for their party conventions. The whole delegate-selection and convention assemblage is loosely referred to as the "primary" in the popular press.
Yes, they are.
> They are private intra party affairs.
That wouldn't stop them from being elections, but primaries are public affairs carried out by the State. (Caucuses are more like you describe, but even they often have state involvement.)
> caucuses in US primaries
Caucuses are not in primaries, they are an alternative to them.