I would say both. If you have two varieties on one tree they will bloom at different times according to the variety. If you have two varieties with different times to first fruiting they fruit in a different number of years, but if you graft to a mature tree the fruiting will be sooner than if you graft to a whip rootstock.

Thanks John, a little clearer please.

I have 5 variety of Japanese plums, if I graph a branch of my earliest bloomer, onto a branch of a late bloomer tree, will the branch bloom the same time as its parent tree, or change bloom time closer to the root stock tree?

I don't think you'll change the bloom time. One thing that's generally accepted to change the bloom time is to find a micro-climate on your property and plant one there. Or perhaps use a lot of ice.

I think tho if you want to try this it wouldn't be a waste of time. Let's say you did change it, by one or two days. You may get thru a frost that the tree your scion came from lost it's crop. And if it doesn't you have a back up for that variety on a 2nd tree.