Term for same root word but words with different meaning

There are actually lots of these. They are called doublets.

My favorite example, which is not mentioned on that Wikipedia page, is the following:

Genre, gender, generic, and genus all come from the Latin genus meaning "kind/class" (although the word actually goes all the way back to Proto-Indo-European *gen-/*gon-/*gn- meaning "produce, beget, be born").

Just to point out, doublets are cognates within a single language.

My favorite pair is galaxy and lactose, which come from the Greek word for milk, gala. The genitive is galaktos. Apparently, Milky Way wasn't a weird choice of name at all...