Contiguous means sharing a border or touching: the contiguous United States are the 48 states that adjoin each other. Continuous means unbroken, usually through time: continuous rainfall, continuous service. One is about adjacency, the other about no gaps.
The core difference
Both suggest things joined up, but along different dimensions.
- contiguous — sharing a boundary: France and Spain are contiguous.
- continuous — without interruption: a continuous hum, continuous employment since 2019.
Continual, the third word
Continual means repeatedly, with breaks — continual interruptions come again and again. Continuous means genuinely without stopping. A continual noise pauses; a continuous one does not. This distinction is worth more than the first one in most writing, because misusing it changes the picture entirely.
Where you meet contiguous
Chiefly in geography, law and property. "The contiguous 48" is the most common encounter, and it is precise: Alaska and Hawaii are excluded because they touch none of the others.