First, the pronunciation: The first syllable of ‘miss’ is pronounced like the word ‘miss’, while the second sounds like the ‘ive’ in ‘massive’ and ‘passive’. The stress is on the first syllable. A missive is a longish letter, often official, sent by someone. It is usually sealed and contains ‘private’ information. The word is considered rather old fashioned, and is mostly used in literary contexts; in informal contexts, it is used humorously.
Example: After the meeting, the Ambassador sat down and wrote a five page missive to the President.
The word ‘missive’ comes from the Latin ‘missus’ meaning ‘to send’; missives are usually sent to individuals. ‘Letter’, on the other hand, is a general term and it can be sent to individuals, companies, organisations, etc. It may deal with business or private matters.
Source: “The Hindu” – Know Your English Column – Feb 05, 2008