Supose we have this scenario:
Why the Connect vertices action has no effect but the Make Edge/Face action does?
In the proposed scenario it's hard to see the difference, so to better demonstrate it I used side of the cube.
The tool will cut through exhisting geometry based on selected vertices which belong to the same face (so if I selected 3 vertices where one vertice per face, there wouldn't be any effect)
The result of using Connect Vertex Path command (J). The order of selecting vertices is important; whether vertices belong to the same face is not. The adjacent faces were splitted, becoming tris now.
Make Edge/Face (F) will simply create new face there atop of exhisting one, not splitting anything.