noun
Refers to the line of descent from ancestors; often used in historical or formal contexts.
彼は名門の世系に生まれた。
He was born into a distinguished lineage.
noun
Can refer to a genealogical chart or the study of family history.
祖父が家の世系を調べている。
My grandfather is researching our family tree.
家系 is more common and refers to family lineage or pedigree, while 世系 is a rarer, more formal term often used in historical or genealogical contexts.
系図 specifically means a genealogical chart or family tree diagram, whereas 世系 can refer to the abstract concept of lineage as well.
Compound of 世 (generation, world) and 系 (lineage, system). The exact historical derivation is uncertain, but the word is conventionally associated with family lineage.