Essentially, different mesh topoloogy but same geometry means different arrangement of the triangles but still have the same shape. So the points are in the same location while the edges are organized differently.
Same mesh topology and different geometry means exactly the opposite. The edges are connected to the same points but the points are in different places.
So same geometry, different topology = points in the same plaes.
Same mesh topology, different geometry = edges connected to same points but points in different places.

leonxu1

Another way to view "same topology" is that, if we look at the mesh as a graph, the graph does not change. Then things like vertex degrees and connectivity do not change. Edge flipping, mentioned later in this lecture, is an example of changing mesh topology.

Essentially, different mesh topoloogy but same geometry means different arrangement of the triangles but still have the same shape. So the points are in the same location while the edges are organized differently. Same mesh topology and different geometry means exactly the opposite. The edges are connected to the same points but the points are in different places. So same geometry, different topology = points in the same plaes. Same mesh topology, different geometry = edges connected to same points but points in different places.

Another way to view "same topology" is that, if we look at the mesh as a graph, the graph does not change. Then things like vertex degrees and connectivity do not change. Edge flipping, mentioned later in this lecture, is an example of changing mesh topology.