Yes, and males go through puberty a little later than females. The difference between child and adult, traditionally across most cultures, starts at a recognition of the ability to reproduce. Aside from some outliers, females begin to be able to reproduce consistently a bit after their first period, and males around the ages of 15-16. In scientific terms, physical adulthood begins after puberty is over (which varies a bit from person to person, sure, but is plenty measurable) and mental adulthood begins after the mid 20s, when the majority of humanity has finished forming and developing most brain structures. Scary to think that the part of the brain that contributes to decision making might not be fully formed in some people until they are 25, isn't it. Heck, in some people, it isn't finished until they are 30.
However, aside from the biological perspective, how adulthood is defined is pretty much arbitrary and culture bound.