It's the same thing.
Millennial makes a lot more sense than Gen Y because each previous generation had its own distinct name (silent, greatest, baby boomer, gen x) and millennial follows that tradition.
It's totally meaningless because the start and stop dates are all arbitrary anyway. I think 1981 is the starting point. I remember seeing a clickbait headline that said "there are more millennials now than any other generation" like it was supposed to mean anything.
I enjoy belittling my fellow millennials because they simultaneously hold the beliefs that they are the best people to have ever walked the earth yet they are hapless victims who can do nothing to change their situation around.