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Types of Official Correspondence. I am assuming that the term "official" refers to "government". Thus, types of government correspondence.

1) Official Letters - generally used to communicate within government or semi-government offices 
2) Demi-Official Letters - generally used to communicate with a sender and receiver who has a personal relationship. This is to used as a friendly letter in an official capacity.
3) Inter-Office Memo - used to communicate with the receiver who is in the same office or department as the sender
4) Endorsements - a copy of an official letter forwarded to other departments as it was simultaneously sent to the intended recipient.
5) Circulars - letter being addressed to all or majority of the departments and is circulated to be read by all its intended recipient.
6) Notifications - formal announcements given to the general public to share salient information
7) Resolutions -  letter containing the decision made by the government or higher authorities on any given subject that it meant for publication
8) Press Release - important resolutions or announcements from the government given to the press or media for public dissemination