Route vs. chaussée
Both route and chaussée refer to roads for vehicles, but they focus on different aspects of the infrastructure. The word route is the general term for a road connecting different places, while chaussée refers specifically to the physical paved surface where vehicles actually drive.
Route
The word route is the general and most common term for a road. It refers to the entire road infrastructure connecting towns or cities, and it can also refer to the journey itself or the abstract concept of a path.
Nous avons conduit toute la nuit sur une route déserte.
(We drove all night on a deserted road.)
La route entre Paris et Lyon est souvent très fréquentée en été.
(The road between Paris and Lyon is often very busy in summer.)
Ils ont construit une nouvelle route pour contourner la montagne.
(They built a new road to bypass the mountain.)
C'est une très belle route qui longe la côte sauvage.
(It is a very beautiful road that runs along the wild coast.)
Nous devons prendre la grande route pour arriver plus vite.
(We must take the main road to arrive faster.)
Chaussée
The word chaussée has a more technical and physical meaning. It refers strictly to the drivable surface of the road, often called the carriageway or roadway in English, and it specifically excludes the sidewalks, shoulders, or ditches.
Les piétons ne doivent pas marcher sur la chaussée pour des raisons de sécurité.
(Pedestrians must not walk on the roadway for safety reasons.)
Il y a un nid-de-poule dangereux au milieu de la chaussée.
(There is a dangerous pothole in the middle of the road surface.)
La chaussée est rétrécie sur deux kilomètres à cause des travaux publics.
(The carriageway is narrowed for two kilometers due to public works.)
Le véhicule accidenté a été rapidement dégagé de la chaussée.
(The crashed vehicle was quickly cleared from the road.)
La pluie verglaçante a rendu la chaussée extrêmement glissante.
(The freezing rain made the paved surface extremely slippery.)
Summary
To put it simply, you travel to another city using a route, but the tires of your vehicle physically roll on the chaussée. Use route when talking about the overall road, the direction, or the journey. Choose chaussée when you need to be precise about the physical paved area meant exclusively for vehicles, often to contrast it with the sidewalk.