How to achieve hard timeout and soft timeout with cookie?

A session timeout is an important security control for any application. It specifies the length of time that an application will allow a user to remain logged in before forcing the user to re-authenticate. There are 2 types: Soft Session Timeouts and Hard Session Timeouts. The former will timeout only when user idling after certain time, the latter will timeout no matter idling or not. Cookie is similar to session, I wanna know if there is a similar timeout difference?