If you have the same topology, even the vertex indexes, it is relatively easy:
You can use transfer attribute in Index mode:
The problem may occur if you have the same topology, but the indices are messed up. In this case you can try to use Transfer the vertex order add-on:
https://bartoszstyperek.gumroad.com/l/copy_verts_ids
If two meshes have different vertices positions use editmode Copy vert ID from sidebar:
First you need to select two, adjacent faces on source mesh - copy mesh id's, and then, select two similar faces on target mesh and paste IDs. Operation has to be repeated for each island (disconnected mesh parts) separately.