Query is about the legal force and legal definition of stuff that is still (quaintly) signed and delivered with due aplomb somewhere to someone, sometimes for photo ops in the White House, many times not, in secret or military decisions and orders (in the normal use of the word) that we’re told about that “come from the President.”
Are there are a set number and type of these?
Nixon’s resignation letter, for example, is sui generis, but other “types of decisions” are classifiable, and perhaps carry important distinctions and procedures.
The President and his staff can name his written orders whatever he wishes. There are all kinds of different types, and they have changed over time. Executive Orders are the best-known modern ones (the subject of a new column by the Perfect Master: How powerful are presidential executive orders? - The Straight Dope). As Cecil notes, many of what are called EOs today were called something else at the time.