Both "contiguous us" and "continental us" are correct terms for referring to sets of US states, even though they are mistakenly often used interchangeably in casual talk:
"On May 14, 1959, the U.S. Board on Geographic Names issued the following definitions based partially on the reference in the Alaska Omnibus Bill, which defined the Continental United States as "the 49 States on the North American Continent and the District of Columbia..." The Board reaffirmed those definitions on May 13, 1999."
https://simple.wikipedia.org/wiki/Continental_United_States
"The contiguous United States, also known as the U.S. mainland, officially referred to as the conterminous United States, consists of the 48 adjoining U.S. states and the District of Columbia of the United States in central North America."
https://en.wikipedia.org/wiki/Contiguous_United_States
"Continental" is also a casual way to refer to European things, but that's a different overloading of the term. Continental is not confined to meaning "European", except where the context implies so (e.g. "continental philosophy", or "continental breakfast"). A leftover from the British refering to Europe as "the continent", it being the nearby continental body next to them.
