I think the vertex order matters in terms of morphing between two meshes. It’s not automatically determined. E.g. the first vertex in mesh A will correspond to the first vertex in mesh B. The morph will just interpolate the positions and it doesn’t have any opinion about initial position vs final position. If you take two meshes that have different vertex counts, and were created separately, it won’t work smoothly.
Generally I’d suggest using deformation tools on one mesh, in order to get the morph shape for the second. This ensures that there’s the same number of vertices in both meshes, and the positions correlate.