Primary elections are held to see who will represent the party in the general election. Every state has their own rules regarding elections. Some cross register to vote for a weaker candidate for the opposite party. Party affiliation of the voter doesn't factor in the general election.
"the shooter was a registered Republican"
Many talking heads in the media were telling Democrats to register as Republicans so they could vote against Trump.
Registration means nothing. He also donated $ to Act Blue.
How does that differ from just voting for a democrat?
Depends on the primary election.
Primary elections are held to see who will represent the party in the general election. Every state has their own rules regarding elections. Some cross register to vote for a weaker candidate for the opposite party. Party affiliation of the voter doesn't factor in the general election.
Cross-registration tends to make you ineligible for primaries.