MST finds the cheapest way to connect all nodes. You run it once and get a tree.
DSU answers connectivity questions dynamically. You can add edges one by one and check if two nodes are connected after each addition.
If you need the minimum cost tree, use MST. If you need to track connectivity as edges arrive, use DSU. Note that Kruskal's algorithm for MST uses DSU internally to avoid cycles. These two tools work together naturally in many problems.