Prove that a graph cannot have two distinct spanning trees

Question

Prove that a graph cannot have two distinct spanning trees.

I'm confused with this proof. More so that I think I'm confused as what distinct in this context means? Initially I thought it was that these $2$ possible spanning trees cannot share the same edges, but in fact, distinct trees may still share some edges.

Any sort of clarification on this would help me a lot. Thanks

Answer 1

Here's $K_4$ with two completely edge-disjoint spanning trees shown as red edges and green edges:

Here's $K_6$ with three edge-disjoint spanning trees: