It's definitely not just "responsible person who can take care of themselves", with adulthood, shame and hubris decline and pride and well-being increase (thanks, Psych Today).
For the past 200 years, age 16 has been considered a big milestone, and has been thought of as "young adulthood".
At 14, a page became a squire, till he was 21, when he became a knight.
Cultural and legal expectations aside, basic adult thinking capabilities are reached about 15 years.
EDIT:I am speaking of emotional maturity level here.
I am asking is an a

dult the fully developed (early 20's) or is it late teens (16+)?
Somebody that has learned the society rules and moves easily inside them.