Difference between J hotkey and F Hotkey

Good question! In a picture:

Another example:

The Faces in the left Circle were made with F, filling the space between 2 Edges five times. J wouldn't have been able to do that at all.

Yeah Martin put it perfectly with the pictures. It's in the name, right? F fills, J joins, it even starts with their respective letters. If you want an analogy, it's as if you are walking in the side walk, it's a lovely day, birds are chirping, the sun is out but not too hot, and you suddenly stop because you came across a part that has been worked on recently and the cement is still mushy. There's yellow lines of Do Not Cross, but you're an outlaw and you decide to go straight through the cement.

Now if you cross the cement with F, you will get to the other side without leaving footprints, because you just filled in the gap without minding what's in between. You can see it in the picture of Martin's circle examples, the one that's made with F, the newly created edge goes from one red vertex dot to the other and it doesn't take into account all that's in the way. Its just "filled" the space in between. It's going over all of the edges it has underneath without interacting with them.

And if you cross the cement with J it will leave footprints in its path, you can see it in the J circle where every time the newly created edge encounters another edge, it creates a new vertex, see the red vertex dot where edges meet? So it leaves that footprint, it "joins" things in it's path as it goes along.