Can you give me a good explanation of the differences between assigning someone as a delegate and giving him or her permission to a folder?

The main difference is that using Tools, Options and setting permissions on the Delegates tab also grants the delegate Send On Behalf Of permission on the mailbox in Active Directory (AD). The user can then send messages as if he or she were the mailbox owner, and the From line on such messages will read From <sender> on behalf of <mailbox owner>. If you want to allow only folder access, without letting the user send on behalf of the mailbox owner, right-click the folder, choose Properties, and set access on the Permissions tab. You also need to use the Properties dialog box when you want to allow access to any folders other than Inbox, Contacts, Calendar, Tasks, Journal, or Notes.