They name the same thing: the paved path for pedestrians at the side of a road. In British English it is the pavement; in American English it is the sidewalk. If you are writing for a British audience, use pavement, and remember that pavement can also mean any paved surface, including the road itself.
The core difference
Pavement is the British word for the paved path alongside a road, while sidewalk is the American word for the same thing.
- pavement — the paved path for pedestrians beside a road, in British usage; also any paved surface: Watch out, there's ice on the pavement this morning.
- sidewalk — the American word for a paved path alongside a road, reserved for pedestrians: Children were skateboarding along the sidewalk.
How to tell them apart
The simplest way to remember the split is by dialect rather than meaning: British English speakers say pavement, American English speakers say sidewalk, and both describe the same strip of paved ground for walkers. Pavement comes from the Latin pavimentum, a beaten or paved surface, from pavire, to beat or ram down — the same root that gives us pave.
The mix-up usually shows up in travel writing or fiction set in another country, where an American character saying pavement, or a British character saying sidewalk, can sound out of place. It is worth noting that pavement has a second British sense too: it can refer to any paved surface, including the road surface itself, as in a truck skidding across a wet pavement.