I am reading this page:
https://en.wikipedia.org/wiki/Partial_cube
They say that a partial cube is a graph that is isometric to a subgraph of a hypercube. I know that isometric in this context means that there exists a mapping between the vertex sets that preserves the graph distance. Is this equivalent to saying that a partial cube is a graph that isomorphic to a subgraph of a hypercube - or is there some detail I am missing?