This is very alien to me, also not from the US. What is party affiliation? And voter registration?

Like in my country, there is a "vote-registry", which is basically only relevant if you move out or back into the country. It is a "should the government include you to be able to cast a vote" , which is associated with your ordinary government registrerd address. All party "affiliations", or they are memberships here, are handled by the parties themselves.

Is party affiliation like memberships but centrally registred with the government? Is voting registration not something which is default, but something you have to... Apply for? How is the party affiliation and voter registration linked? You have to include who you intend to vote for?