Why don't Faces stay connected to vertices ?

I am confused about why the Faces do not follow the Verts at random here. On the Lower Right I moved the VERT and the faces followed. But on the top its different. Why don’t the faces follow the vert on the top ?

SNAPPALY.blend (417 KB)

Because they’re not connected. There are 6 vertices connected with 10 edges and form 5 faces in total. The mesh elements shown on the right aren’t connected to the rest but are overlapping.

How were you able to separate the two overlapping meshes ? I welded vertices before I added faces but maybe I needed to remove duplicates before adding the faces. ? I am somewhat confused about these basics. I have watched many videos and went through a lot of tutorials. I may have skipped some Elementary beginner basics though.
Thanks JA12

I selected the big faces and separated them, P -> selection. The rest are connected in a sense that selecting linked will select all, they’re just not all connected but overlapping, as moving the faces before separating shows.