If you look for a family law attorney you’ll typically find law firms that handle cases related to divorce, child custody, alimony, spousal support, etc. It’s not uncommon for a custody attorney to also handle divorce cases and vice versa, which is understandable given the overlap between both fields.
That said, technically speaking the definition of family law is simply “the area of law that deals with family matters and domestic relations”, according to Wikipedia. The Oxford dictionary and other sources define it similarly. Under that definition, family law also includes marriage contracts, civil unions, domestic partnerships, child adoption, and more.
In other words, a child adoption attorney can technically be classified as someone who practices family law, because they do. But you will seldom see that type of attorney be referred to as a family law attorney. That term is reserved for attorneys that deal with matters related to marriage, marriage dissolution, and child custody.