What you are describing (late 90s, early 2000s onwards) is the definition of generation Z:
https://en.wikipedia.org/wiki/Generation_ZMillennials are the group born in the 80s/early 90s and were introduced the internet at some point while they were growing up, rather than it having always existed as part of their life.
Nobody is really sure what generation Z is like yet, but they are definitely different than millennials.