Question: Are votes counted in primaries more quickly than in general elections

I am wondering whether votes are counted faster in Republican or Democrat primaries. Or whether they are counted faster in primaries or general elections. There is always the claim that certain districts will hold back on releasing their votes until they know the number of votes need to win a close election. If so and if one party is more likely to do it than another party, in close elections there should be a difference across parties in terms of how quickly votes are reported.