In vertex cover you want to select vertices, that cover all the edges, this means if an edge is not adjacent to the selected vertex, it is not covered (provided, it has not already been covered by another selected vertex). In dominating set, you want to select vertices, that cover all adjacent vertices. e.g., for the following edge set (a,b), (b,c), (c,a), in vertex cover, if you select a, it will only cover (a,c) and (a,b). In order to cover (b,c), you need one more vertex. However, for the same graph for dominating set, selection of any one vertex is enough as the other two are adjacent to that vertex. I hope it is clear now.