The term that describes when words have multiple meanings or shades of meaning is "nuances".
The term you are looking for is "nuances." Nuances refer to the small differences or variations in the meaning, feeling, or tone of a word that give it multiple meanings or shades of meaning. For example, the word "run" can mean physically moving quickly, managing or organizing something, or operating a machine. These different senses of the word "run" represent its nuances.
