With admin option is used for system permission authorization, and with grant option is used for object authorization.
However, when a user is granted system permissions with the with admin option, the user can grant the system permissions to other users or roles, but the user's system permissions are revoked, the system permission granted by this user to other users or roles will not be invalid due to propagation. For example, if you authorize system A to create session with admin option, then a grants the create session permission to system B, however, when the Administrator revokes the create session permission of a, B still has the create session permission, but the administrator can explicitly revoke the permissions of B create session, that is, directly revoke create Session from B.
When the with grant option is used for object authorization, the authorized user can also grant this object permission to other users or roles, the difference is that when the Administrator revokes the permission of a user object authorized by the with grant option, the permission will be invalidated due to propagation. For example, grant select on table with grant option to, user A grants this permission to user B. However, when the Administrator revokes the permission of user A, the permission of user B also becomes invalid. However, the administrator cannot directly revoke the select on table permission of user B.