Before revision: In the k-Vertex Disjoint Shortest Paths problem, a set of  terminal pairs of vertices \{(s_i,t_i)\mid 1\le i\le k\} is given and we are asked to find paths P_1,\ldots,P_k such that each path P_i is a shortest path from s_i to t_i and every vertex of the graph routes at most one of such paths.
After revision: In the k-Disjoint Shortest Paths problem, a set of terminal pairs of vertices \{(s_i,t_i)\mid 1\le i\le k\} is given and we are asked to find paths P_1,\ldots,P_k such that each path P_i is a shortest path from s_i to t_i and every vertex of the graph routes at most one of such paths.