Sharing is just that - you share your folders with others at the specified permissions level.  There are no other implied abilities when sharing.

When giving someone Delegate Access, you set the permissions level, but they can also accept meetings on your behalf and are granted "send on behalf of" permission to your mailbox.

The key difference in managing the Calendar:

When simply sharing your Calendar with another user, even if you give him or her "Editor or Owner" access, the person will not receive meeting related emails that are sent to you. You can allow that person to create meetings on your behalf and make other changes to your Calendar, but you will be responsible for accepting and declining meetings.

If you instead make someone a Delegate, that person will also receive copies of meeting related emails (invitations and responses) sent to you if you so choose.  In that case, both you and your delegate have the ability to accept or decline meeting requests on your behalf.

The key difference with respect to mail:

When simply sharing your Inbox with another user, even if you give him or her "Editor or Owner" access, the person cannot send or respond to email on your behalf.

If you make someone a Delegate, that person is also given the ability to send and respond to email on your behalf.