What are these parties in the NY governor primary?

Factual Questions
1

I was reading this article about the NY governor primary in the NY Times (reg required), and I have no idea what they’re talking about with these party names. Here’s some snippets:

Huh? Isn’t this the Democratic primary?

2

New York has a number of third parties including the Liberal party and the Conservative party. Each of them nominates candidates for office, but sometimes their nominees are also major-party nominees. Accordingly, the Republican candidate often garners the Conservative party nomination and the Democratic candidate often gets the Liberal party nomination.

3

Like Acsenray states, New York is one of the few states to allow what are called cross-endorsements, where a candidate can run as a member of more than one party. Usually, the smaller parties just endorse one of the two major party candidates, especially for statewide office, but not always, and lack of an endorsement from minor parties can hurt the major candidates, even though the minor parties usually can’t successfully run candidates themselves. Exceptions do exist, of course, most notably, that of Jim Buckley, who, in 1970, ran as the Conservative candidate for U.S. Senate against a Democrat and a liberal Republican and won.

4

For more information, see , for example, http://www.cnn.com/1999/ALLPOLITICS/stories/12/08/ny.senate/

5

When it’s primary day, all parties get to have primaries, not just the Democrats. Parties don’t have to have primaries at all, to be sure. They can select a candidate through party conventions. But if enough petition signatures are turned in, a primary can be forced. Golisano has been trying to get his name on the ballot on any line – a line on the election ballot being alloted to each party – just so that his name appears somewhere on the ballot, no matter what party it is attached to.

Yes, this system is extremely weird to people in other states. But on the good side, NY allows only members of a party to vote for candidates of that party in a primary. I find it bizarre that other states allow anyone to vote in a primary for anyone. Why should registered Republicans be allowed to pick the Democratic candidate and vice versa?