I think the best answer to this question is to point you to the definition of a presidential record in law; 44 U.S.C § 2201 (2) states:
The term “Presidential records” means documentary materials, or
any reasonably segregable portion thereof, created or received by the
President, the President’s immediate staff, or a unit or individual of
the Executive Office of the President whose function is to advise or
assist the President, in the course of conducting activities which
relate to or have an effect upon the carrying out of the
constitutional, statutory, or other official or ceremonial duties of
the President. Such term—
- (A) includes any documentary materials
relating to the political activities of the President or members of
the President’s staff, but only if such activities relate to or have a
direct effect upon the carrying out of constitutional, statutory, or
other official or ceremonial duties of the President; but
- (B) does not
include any documentary materials that are
- (i) official records of an
agency (as defined in section 552(e) of title 5, United States
- (ii) personal records;
- (iii) stocks of publications and
- (iv) extra copies of documents produced only for
convenience of reference, when such copies are clearly so identified.
So yes, the answer is that everything put on paper relating to the matters in subsection (A) falls under this definition, provided it is not subject to the exclusions in subsection (B). Note the exception made for "personal records", which is defined later in that section - an example given is "diaries, journals, or other personal notes serving as the functional equivalent of a diary or journal which are not prepared or utilized for, or circulated or communicated in the course of, transacting Government business". In addition, § 2203 (c) states:
During the President’s term of office, the President may dispose
of those Presidential records of such President that no longer have
administrative, historical, informational, or evidentiary value if—
- (1) the President obtains the views, in writing, of the Archivist
concerning the proposed disposal of such Presidential records; and
the Archivist states that the Archivist does not intend to take any
action under subsection (e) of this section.
Subsection (e) relates to the Archivist requesting the advice of certain Congressional committees as to whether the record should be retained.
Apart from these exceptions, all records must be retained and not shredded or otherwise disposed of. As a check on the release of secret or sensitive documents, an outgoing President may determine a time period not exceeding twelve years during which access to a specific record should be restricted (so long as the record falls in certain categories - see § 2204). Additionally, all other records are only subject to public release under 5 U.S. Code § 552, which contains plenty of provisions by which the publication of sensitive documents may be restricted.