Consider your own record or paper trail. Records probably exist somewhere for your birth, school attendance and grades, school year books, photographs, a mention in newspaper articles for various reasons, social security information, marriage, divorce, children, jobs, church, medical/hospital, drivers license, taxes paid to various government entities, rent a house or apartment, purchase a house or land, credit history, military service, a will, a living will, etc. These records, if still existing, are in places scattered all over the U.S. Put all of the available information together for an individual and you get quite a portfolio of "a person" and "a life".
Basically, it all boils down to this:
Genealogy is proving that a given person is the biological child of another person. Genealogy is like "a tree in winter" or "a skeleton". It is a pedigree showing how people are related.
If genealogy were a college degree, it would be a Bachelor of Science (B.S.)
Family History is adding all of the other details about a person. Family History is like "the tree leaves" or "the muscle and flesh on the skeleton". It is a collection of the stories of all the persons in the same family.
If family history were a college degree, it would be a Bachelor of Art (B.A.)
NOTE: Throughout the rest of this document, when the word “genealogy” is used it can also refer to “family history”