What's the difference between travelling salesman problem (TSP) and Chinese postman problem (CPP)?
For me, both wants go to a destination, and then back.
The travelling salesman problem is about going to each city once and taking the shortest route.
The Chinese postman problem is about getting a path from each city to each other city.
E.g., with points A, B, C, and D, the travelling salesman could go A-B-C-D-A, but the Chinese postman would go need a route that had A-B and A-C and A-D, etc.
The travelling salesman route does not have a direct between each point (in the above example there is no A-C link).
Each city is a vertex and each inter-city link is an edge. So, I think I'm just restating Xodarap's answer.