What is the difference between the order of the local error and the global error of a numerical method to solve a PDE?

This seems an interesting question. But I need some clarification on the question. Are you looking for the definition of the "order of global error", or are you looking for the "difference between" the orders of local and global error?

I need both of these.

Local error at t(n+1) is calculated after running a numerical method for one step starting from the exact solution at the step t(n). Whereas global error is accumulated after running the method for the entire time, often defined as y(n+1)-y(x_{n+1}) In terms of order: If the local error is O(h^p), global error becomes O(h^{p-1}).