Shem is traditionally identified as the son of Noah through whom the Israelites descend.
Genesis 10 lists descendants of Noah's three sons in the Table of Nations. Genesis 11 then follows Shem's line through several generations to Abram, later called Abraham. In biblical genealogical tradition, Abraham is the patriarch of the Israelites through his son Isaac and grandson Jacob.
Shem is therefore connected to the Israelite ancestry through the genealogy leading to Abraham, not because the Flood account says that all of Noah's descendants had the same later identity. Ham and Japheth are also presented as ancestors of other peoples in the biblical table.
The term “Semitic,” used in modern historical and linguistic contexts, is derived from Shem's name. However, linguistic classification and biblical genealogy are related only indirectly, so the terms should not be treated as exact synonyms.