A business letter and memo are both styles of communication. The letter is a more formal thing, with fairly well prescribed format including things like an internal address, generally using full names, title, etc.,, salutation and closings. The memo is a much less formal communication, generally for audiences that communicate frequently with each other. The format has much more leeway (generally just a to/from/date/subject). Abbreviations are fine as is a more casual discussion format.
The email and fax are both different methods of electronically sending/delivering those communications.
Only recently has the use of either electronic method been considered acceptable (and is still disputed by some) for delivering the formal business letter. Some questions still exist about if the electronic means is adequate for Legal things too. I would suggest it is never a good method for anything sincere or personal.