Basically family is a group of people connected to each other by genes or blood relation. Its possible that a person who doesn't have any blood relation can become a member of a family - Example include relation with wife - as a wife comes as a startup of a new family, adopted child etc. Sometimes people mutually stay along with each other without having any sort of blood relationship but have good understanding among them.
In the real world family are grouped into various types :
* Conjugal Family or Nuclear Family
Nuclear family you must have heard this term in matrimonials and all. This kind of families mostly has parents/guardians and their children. Generally in the group of 4 -6 family members.
* Consanguineal Family or Joint Family or Extended Family
This is basically a combination of families - may be a combination of family trees in few cases. For example the mom, dad, their children, grandma, grandpa, greatgrandma, greatgrandpa, paternal uncle, paternal uncle's family, other causes -- it can be in any permutation and combination. This is quite common in the ancient world - most commonly regarded as joint family. Yes for survival various responsibilities are divided into members by mutual agreement (in the aspect of finance, cooking, caring etc)
* Single Parent Family
In this kind of family basically the children are raised by one parent (mom or dad). Yes high divorce rate or death of mom/dad is the cause of this. This is one of the fastest growing families as due to high divorce rate especially in america. Also if the children is raised by a mom then its called matrifocial family.
* Childless Family
These are those parents who doesn't want to have kids - due to many reason such as may be busy in career, want more free time, finance etc.