What's the difference between traveling salesman and chinese traveling?

Graphs are made of edges and vertices. CPP requires a visit to all edges. TSP requires a visit to all vertices.

The Travelling Salesman 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).

EDIT:
Each city is a vertex and each inter-city link is an edge. So, I think I'm just restating @Xodarap's answer.

Keeping it ultra-simple:

The Travelling Salesman Problem is about visiting each city exactly once while returning to the original city (thus walking along a Hamiltonian cycle) and also taking the shortest route among all possible routes that fulfill this criterium (if such a route exists). Finding such a cycle, perforce finding the possibly unique optimal cycle with the shortest distance, is "hard".

The Chinese Postman Problem or Route Inspection Problem is about visiting each road between cities at least once while returning to the original city and taking the shortest route among all possible routes that fulfill this criterium (if such a route exists). A solution that takes each road exactly once is automatically optimal and called an Eulerian Cycle. Finding such a cycle is "feasible".