Family lines have been recorded for hundreds of years as a way to track the purity of characteristics, family relationships and ownership. As humans we rely on our ancestral family trees to identify family and pedigrees to identify characteristics. We use these charts differently for animals as well, as we occasionally need to track particular elements of an animal's breed through its ancestry.
Merriam-Webster sites an equivalent between "family tree" and "genealogy," making the family tree not just a chart to track family members, but the relationships between these family members as well. The written chart of a family tree shows all, or most of the relationships between marriages, offspring and siblings.
A pedigree refers specifically to qualities of a family ancestry, as opposed to referring to its simple existence. Generally the word "pedigree" connotes positive elements or ideal lineage but can refer to unwanted characteristics as well. The pedigree chart shows the relationships of these particular qualities through an ancestry, following it to its originator as proof of purity.
Uses of Family Tree
A family tree can be used to prove ownership or relation, or simply as an identifier of family for the curious. They are often helpful to track particularly complicated family relationships in a visual manner, where labels and words can be confusing. Family trees can be ornamental, as well as instructional.
Uses of Pedigree Chart
Pedigree charts are useful to identify the source of characteristics, genealogical traits and as proof of quality. They are often used to show the purity of breed of pure-bred animals and record extra information such as the birthplace of relatives. Pedigree charts often show only the parental lines instead of all relatives.