I can't get the difference between this two problems, which seem equal to me.
But, for the former, a polynomial solver is known, while, for the latter, it is not.
EDIT - References:
The quickest transhipment problem - by B. Hoppe and E. Tardos The quickest multicommodity flow problem - by L. Fleischer and M. Skutella
In the former paper, which has polynomial solution, authors explicitly refer to integral flows. While in the latter one, authors state that "the complexity of the quickest multicommodity flow problem is still open. It has neither been proved to be NP-hard nor is it known to be solvable in polynomial time".