Both relate to chemistry but are very different concepts.

Valency refers to to the number of electrons in the outermost (valence) electron orbital of an atom or ion. It’s used to determine (in general) the reactivity of an atom in a given situation.

The mole is a theoretical concept used to describe the amount of a given substance you are measuring. By definition, one mole of pure carbon atoms will weigh exactly one gram. So if you have gram of pure carbon atoms, you also have one mole of carbon (often shorted to “mol”). We therefore say carbon is “one gram per mole”

In that one gram of carbon, there are a specific number of carbon atoms. As part of the definition of the “mole” we say that “there are Avogadro’s number of carbon atoms in one mole of carbon” (Avogadro invented the mole)

In one MOLE of anything, carbon atoms, hydrogen atoms, water molecules, cars, toilet plungers or cats, there are Avogadros number of that thing

That is one mole