A lot of shorthand gets used here and on other political websites. It assumes a certain level of familiarity with the American political process that I have observed is often lacking. A little background on myself: I am an underemployed adjunct political science professor and a lawyer whose main area of research is election law. As someone who teaches American government to undergraduates, a strong knowledge of the fundamentals is crucial to understanding how and why politics works the way it does. I figured I can help contribute to this understanding in as nonpartisan of a way as possible. My first topic: the law of primaries.
So without further ado, let's look at the types of primaries in the U.S.
First of all: what are primaries? Primaries are (typically) used to select a political party's candidate for an office. In that sense, they are intra-party devices used to determine who will be represent the party's nominee on the ballot. In recent history the major division has typically been thought of as being between open primaries - those primaries open to all individuals, regardless of party affiliation - and closed primaries - those primaries limited to registered members of a party. As we shall see this is a rather simplistic and inaccurate assessment of primary law. Furthermore, the rise of the so-called "jungle" primary further complicates this.
Open: At its most basic level, open primaries are those where any voter, regardless of registered political affiliation, can vote in any party's primary. States with open primaries tend to disincentivize formally registering as a member of a political party because such registration is not necessary to participate in the primary process. At the same time, open primaries are often notorious for encouraging opposing party members to vote in their rival party's primary for two reasons: either in the hope that a less electable candidate wins the party's nomination (such as George Wallace winning Michigan's Democratic primary in 1972 aided by Republican crossover voters); or in the case of presidential primaries, forcing the active primary process to be continue indefinitely (such as the so-called Operation Chaos from the 2008 Democratic presidential primary, intended by conservative leaders to drag out the Democratic primary).
Semi-Open: Semi-open primaries are very similar to open primaries in most aspects. Like open primaries, a voter need not be a registered party member to vote. Unlike open primaries, semi-open primaries require that the voter select a particular party's ballot when going to vote; in open primary states, both parties' nominees are on the same ballot and the voter does not have to inform the officials which party's primary he or she is voting in. Besides this point, semi-open primaries are the same as open primaries.
Closed: The major historical alternative to open primaries are closed primaries. Closed primaries require that the voter is a registered party member prior to the election. Opposing registered party members and those who are not registered as being a party member are not allowed to cast a ballot. Closed primaries are often favored by party elites because they ensure that only the party's members have a say in determining who wins the nominations. At the same time, closed primary systems in heavily partisan districts tend to encourage the election of more ideologically extreme candidates because the primary, rather than the general election, becomes the decisive forum for the election.
Semi-Closed: Semi-closed primaries are similar in most respects to closed primaries. The major exception here is that semi-closed primaries allow voters to register as a member of the party on the day that they cast a ballot. This is different from closed primaries, where such a decision must be made in advance of the election.
Jungle/Top-Two/Nonpartisan Blanket Primary: These are all different names for the same type of primary, which I will refer to as jungle primaries for the remainder of this description. In a jungle primary, all candidates, regardless of party, are placed on the same primary ballot, and the top two vote-getters, regardless of party, advance to the general election. Thus it is possible that in very conservative districts, two Republicans will compete against each other in the general election, and vice versa for Democrats in very liberal districts. (In some states like Louisiana, a candidate who wins a majority in the primary wins the election and avoids the general election entirely, but this is not universally true). Jungle primaries are often thought to better reflect the partisanship of the district in the general election, allowing heavily partisan districts to have a meaningful general election (as opposed to such districts under other formats, where the general election is often a formality). At the same time, such systems can lead to drastic splits in voter support among the dominant party's members, allowing the minority party to place two candidates on the general election ballot with a very small amount of support (such as what happened in California's 31st congressional district in 2012).
A note on blanket primaries: Blanket primaries are systems where a voter can vote for one party in one primary, and another party in a different primary. The Supreme Court ruled in California Democratic Party v. Jones that such systems were unconstitutional. Thus for all systems, if you vote in one party's primary for one office, you must vote in that party's primary for all offices, or else your vote will be spoiled.
I hope this post has been informative to the community. More detailed conversations and/or questions on this topic can take place in the comments. The next post in this series will be on the law of redistricting, looking at the Voting Rights Act and the important Supreme Court decisions.