What is the difference between the US and the Contiguous US?

"Contiguous" means the part that's all connected, all parts physically touching each other.
The part of the US in which you could walk or drive to anywhere in it without leaving the country.

Alaska isn't contiguous because you can't walk there without going through Canada.

Hawaii isn't contiguous because you can't walk there at all.

The "contiguous US" is the "lower 48" states.