Late 90s early 00s were the Y2K era, the Playstation era. Thinking in terms of aesthetics and music, 2000s begun properly somewhere in 03/04.There was no tangible shift from the late 90s to the early 00s, everything was just a glossier or more brutal continuation. Only later on could you distinguish the atmospheres and parameters that marked the noughties off from the 90s and the 2010s.
I'd say that 2008 was still aughties, and it feels like the decade only ended in '12. This is again, based largely on aesthetics/music, but IMO after 2008 financial crash it took some time to settle down to new reality. I believe that in financial field there wasn't much investment going on for a while. Contrast that to one of the characteristics of 2010s, which was loose investment money for tech startups, giving birth for that decade's tech boom. Fashion-wise 90s revival was big in 2010s, and it was in full-swing in '16, whereas 2020s has seen the rise of YK2 revival.