Faces / Edges / Verts

When I select 2 edges and subdivide, the edge goes in fine with the existing face.
I was wondering though when I select an edge and subdivide I get a vert. So do that twice and I have 2 verts to join.
If I press F with the 2 verts selected I get another edge. But why does the edge go over top of the geometry?
Is there a command to make that edge part of the existing face, if I do end up doing it that way?
The first way works.
The second way I would like to know because if I botched something up and noticed it later, now I want to fix the hanging edge that I want to be part of the underlying face.

I think you’re looking for “Vertex Connect” = J key.

Thanks, that works. Skipped past it in the vertex menu so many times. I can remember that!