Traditional family: A traditional family has a mum, dad and usually about two children. The day goes to work and the mum stays home and looks after the house and kids.
Nuclear family: A modern family that usually has a parent of both sexes and children, either biological or adopted. Both parents generally work. Sometimes this term is extended to single parent and childless families.
Extended family: Extended families are close knit families that consist of not only parents and children but grandparents, aunts, uncles and cousins, and also foster children. A lot of the time in extended families older relatives (like grandparents) look after the younger kids whilst their parents work.
Foster family: A foster family is when children are taken away from biological parents or legal guardians, and are sent to live with "stand in" parents, generally until a more suitable guardian is found.
Adopted family: Adopted families are when a child is permanently put with parents who aren't their biological ones.
Once they are properly adopted there is no legal difference between adopted children and biological children.
Step family: A step family is when a marriage with children has split up and then one or more of the parents re marry. The new spouse is then called a "step mother" or "step father" to the children, and if there were previous children and/or marriages in both spouses lives, they are now "step brother" and "step sister".
Sibling: A sibling is a brother or sister born to both the same parents as you.
Cousin: A cousin is the child of a brother or sister of one of your parents.
Aunt/Uncle: An aunt or uncle is either the brothers and/or sisters of your parents, and their spouses.
Mother in law/Father in law: A mother/father in law is...