It's exactly the other way around actually, continental US would include Alaska since it's still on the North American continent whereas contiguous US excludes both Hawaii and Alaska. Contiguous US refers to the lower 48 states.

Continental "could" include Alaska (it's even in the official U.S. Board on Geographic Names definition), but in practice when "continental US" are casually mentioned, it's rarely implied as included. Most use it as interchangeable with contiguous.