That's the difference, but it's a pretty big one. The diamond shaped hole makes the stick travel only to the cardinal directions, instead of freely roaming the full 360 degrees. If you put that 4 way actuator on your p360 kit, the stick will only send 4-way data, but it will still feel like an 8-way. If you've never played with a true 4-way before, you won't know the difference. But if you have, you'll miss the tactile feedback it provides.
It's like the scroll wheel on your mouse. A few years ago, there was no such thing, and we all navigated the internet without one, and we were perfectly happy that way. Have you ever pulled out an old wheel-less mouse and tried to switch back? Now that you're used to the extra control, it's hard to do without it. The tactile feedback from the diamond shaped hole gives you extra control.
If you've never had a true 4-way available to try, you can feel the difference I'm talking about if you have access to the Jakk's Pacific TV game sticks.. The Pac-Man one has a 4-way on it, and the Ms. Pac-Man one has an 8-way. Play a bunch of Pac Man, then switch to Ms. Pac.. you'll feel it. Of course, those aren't quite the same as real arcade sticks, but they should illustrate the difference.