My understanding was that Gen Y originally referred to older millennial. At least, as a younger millennial, that's what I always heard them called growing up until the millennial term got solidified. Meanwhile, Gen Z is the name for the people younger than the millennial cohort until someone coins a catchier one.

As an aside, I always thought that the age rage for millennials was about twice as broad as it should be. I don't really find myself identifying with the older members of the cohort.