Contiguous 48 states is a subset of the continental U.S. and refers to the 48 states that are physically connected to each other. This excludes Alaska and Hawaii, which are not physically connected to the other 48 states.
The main difference between the continental U.S. and the contiguous 48 states is the inclusion or exclusion of Alaska and Hawaii. In most cases, when people refer to the continental U.S. they are referring to the 48 contiguous states, but for some specific purposes (e.g., statistical analysis or political representation), it may be necessary to include Alaska and Hawaii.