Millennial was a renaming of gen Y. People born after the turn of the millennium are normally down as gen Z, though I assume someone will come up with a snappier name for that in time. Precisely what their view on avocados is remains unclear.

Note that if you're in the older end of the cohort (mid-30s), there's some effort to rebrand those as 'Xennials', if for some reason you're really bothered by being called a millennial :)

It’s people who became adults around the turn of the millennium, not people born then.

Gen Y == Millennial

This is why there is a Generation X/Millennial "transition" group of people that is sometimes referred to a Xennials[1].

[1] https://en.wikipedia.org/wiki/Xennials

Both Gen Y and Millennials were the generation after Gen X, but different analysts placed the cutoff at different points and around different events. The people who coined the phrase 'millennial' thought that generation started in '82 and ended in '02 while the people who came up with the name Gen Y were, if I recall correctly, placing the cutoffs at '78 and '98 (or thereabouts).

'Millennial' seems to have been the catchier name, so it stuck around more - I think most people who are Millennial or Gen Y are also the other.