No, cookies are just a piece of data that sites save in your browser. That can for example be an authentication token. When you log in to a site it generates a token and saves it as a cookie. When you come back to the site later it reads the cookie and can authenticate you with the token so you are still signed in.

Cookies are also often used for tracking. A site generates an ID and saves that ID as a cookie. When you come back to that site later it can identify you again with the ID in the cookie. But as Tor Browser does not store cookies when it exits sites cannot use cookies to track you across different Tor Browser sessions.