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Supose we have this scenario:

Vertices

Why the Connect vertices action has no effect but the Make Edge/Face action does?

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    $\begingroup$ I'd say Vertex Connect uses exhisting geometry to cut it through, and this doesn't exhist here. $\endgroup$ – Mr Zak Aug 22 '15 at 22:27
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    $\begingroup$ @MrZak That is the answer, you should post that. It's basically a lazy, simplified version of the knife tool. $\endgroup$ – iKlsR Aug 23 '15 at 1:06
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The difference between them is that Connect Vertices tool cuts through already exhisting geometry (just like Knife Tool), whereas Make Edge/Face creates new one.

In the proposed scenario it's hard to see the difference, so to better demonstrate it I used side of the cube.

Connect Vertices

enter image description here

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)

Connect Vertex Path

(I decided to put it also here because for some time I couldn't get the difference) enter image description here

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

enter image description here

Make Edge/Face (F) will simply create new face there atop of exhisting one, not splitting anything.

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