Fatherhood is the state of being a father — the role, not the man himself. You can talk about the joys of fatherhood, or how someone grew into fatherhood. It is a little formal and serious; in warm talk people say being a dad. It covers the whole condition: having a child and living as that child’s father. Though actually, people sometimes use it in a high, proud way, as if fatherhood were a prize, when day to day it is mostly showing up and doing the work.