CONUS is military
shorthand for the
CONtinental
United
States. This
should include
Alaska, but not
Hawaii or any other outlying territory such as
Guam,
Puerto Rico, etc. etc.
However:
The term CONUS has been expanded in U.S. Government use to mean either Continental United States or Contiguous United States. The difference here is really whether Alaska is considered part of CONUS, as it certainly shares the continent but is not contiguous. As indicated above, the U.S. military uses the term to mean 'continental United States' (as an example, see the U.S. Army's Regulation 600-20, 'Command Policy' here - footnote 13 on p. 7 expands CONUS to 'Continental' inline). This is supported by manual JP 1-02, the Joint Publication "Dictionary of Military and Associated Terms" published by the US DoD here. Of course, the real question is whether 'Continental' includes Alaska, because these military sources don't tell us that. Technically by the rules of English, it should, but as we all know, this is the military (right way, wrong way, military way).
Other parts of the DoD use CONUS to mean Contiguous - see, for example, the DoD travel calculator here which explicitly divides CONUS/OCONUS by contiguous, and in this case AK and HI are both explicitly listed as OCONUS.
It's a bit of a mess.