A(n) primary is one in which voters get the ballot of their announced party.

This is called a closed primary. This means that only if you're in a party you can vote for who's going to represent the party in the general elections. For example, members of the democratic party can't vote on who's going to be the republican candidate, and vice versa. You can also be a third party or run as an independent if you get enough support from the public.