There are two types of permissions you can apply through the Control Panel:
Full Access Permissions
Full Access gives a user full visibility of another mailbox, including the ability to edit or delete items.
When a user has Full Access permissions and uses Outlook for Windows, Outlook will attempt to automatically add the other mailbox as an additional mailbox.
Full Access does not allow a user to send as another user, these permissions must be applied separately and there is a tab for doing so.
Send on Behalf/Send as Permissions
Send As allows a user to send as another. An email sent this way will appear to have been sent as the other user. e.g. If User A sends as User B, the recipient will only see the sender as User B.
Send of Behalf allows a user to send as another, but it will show the the original user as having sent it. e.g. If user A sends on behalf of User B, the recipient will see it comes from User A on behalf of User B.
Full access permissions