How is a memorandum different from a letter?

A memorandum or memo is a means of business communication
within an organization, unlike a letter which is used for communication between two or
more different organizations or between a business and its
clients. 

A memo is used to convey a message when
word-of-mouth is not sufficient. It is often prepared somewhat informally as compared to
a letter, which is generally very formal. Memos have less attention to structure,
grammar, formatting and quality of paper. Letters, on the other hand, are written
formally, proof-read to ensure accuracy and avoid even the smallest
mistakes. 

A letter can be as long as needed, whereas a
memo is generally kept short and to the point. 

A memo
generally has a header that states where it is from and the intended recipient, along
with the date and subject. It does not need to be on company stationary. A letter is
always written/printed on business stationary and includes the date, the recipient's
name, designation/title, his/her address, and starts with an appropriate
salutation. 

A memo does not, generally, conclude or
summarize anything and finishes with a work action (a to do activity). A letter
summarizes or concludes the communication, asks the recipient to contact the writer and
ends with thank you to the reader. The sender's name and address are also
included.

Hope this helps.