Not American so I'm curious: couldn't anyone just register as one party and vote in the primaries but then vote the other party at the actual election?
Yes, you can also register with a party and vote in the other party's primary if it's an open primary state. However, you are usually barred from voting twice in a primary, which means you need high confidence in the outcome of your preferred party's candidate to do this. Otherwise, you're throwing away your vote on that party's pick.
EDIT: I had to double check this before commenting, but in some states you don't even register with a party as far as the state is concerned (Georgia, for example, it's been 12 years and I'd forgotten). Though they still have the party primaries.
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Not American so I'm curious: couldn't anyone just register as one party and vote in the primaries but then vote the other party at the actual election?
Yes, you can also register with a party and vote in the other party's primary if it's an open primary state. However, you are usually barred from voting twice in a primary, which means you need high confidence in the outcome of your preferred party's candidate to do this. Otherwise, you're throwing away your vote on that party's pick.
EDIT: I had to double check this before commenting, but in some states you don't even register with a party as far as the state is concerned (Georgia, for example, it's been 12 years and I'd forgotten). Though they still have the party primaries.