Minimum spanning tree vs Shortest path?

Question

What is the difference between minimum spanning tree algorithm and a shortest path algorithm?In my data structures class we covered two minimum spanning tree algorithms (Prim's and Kruskal's) and one shortest path algorithm (Dijkstra's). Minimum spanning tree is a tree in a graph that spans all the vertices and total weight of a tree is minimal. Shortest path is quite obvious, it is a shortest path from one vertex to another. What I don't understand is since minimum spanning tree has a minimal total weight, wouldn't the paths in the tree be the shortest paths? Can anybody explain what I'm missing?Any help is appreciated.

Answer 1

Prim's minimum spanning tree (or Kruskal's) will find the least amount of length required to span the entire undirected graph.

Dijkstra's shortest path algorithm can be used to find the shortest path between two vertices, and not the entire graph (connecting each vertex using the shortest path).