Do Kruskal's and Prim's algorithms yield the same minimum spanning tree?

Assuming the edges are undirected, have unique weight, and no negative paths, do these algorithms produce the same Minimum Spanning Trees?

Found this which states that if all the conditions I mentioned above are met, a graph necessarily has a unique MST. Therefore, in terms of my question, Kruskal's and Prim's algorithms necessarily produce the same result.

StackExchange Computer Science Q#84159, answer score: 14