With admin option and with GRANT option in the authorization

Oracle

When a user is granted system privileges with admin option, he can grant this permission to other users, roles, and do not cascade the permissions that he grants to other users when revoke is granted the user's system privileges. If a user P system permission is granted with the WITH admin option parameter, then a gives the system permission p to User B, and then revoke the P permission granted to a user, at which point the P permission granted to B is not cascaded back, which means B also has P system privileges.

The parameters of the object permission with GRANT option are cascaded to reclaim object permissions. If you grant the A user O object permission with the WITH GRANT option parameter, a gives the O object permission to User B, and if revoke grants the O object permission to a, it revoke the O object permissions that B is granted.

Mysql:

Only with GRANT option in MySQL, a user authorization, a can be granted to other users, when the authorization to a is withdrawn, a grant to other users will not be cascaded back. Note that with GRANT option can also be granted to other users.