2000's baby
A 2000's baby is one who is born in the 2000's (2000-2009). A 2000's kid is one who is born in the 90's (1990-1999).
If you were born in 1990-1999, you are a 90's baby and 2000's kid. If you were born in 2000-2009, you are a 2000's baby and 2010's kid.