Wagyu is the breed of the cow; it can be raised anywhere. "Kobe" is reserved for Wagyu cows raised near Kobe, Japan, following the appropriate "DOC" regulations.
I have a Kroger-owned store near me. They often have Choice steaks for small money, and, being a cheap SOB, that is what I generally "spring for." A couple of times in recent months I scored a grass-fed, organic, prime steak at the same store on sale ("Woo-hoo," for the cognescenti). It looked like Mike's Wagyu picture above. Oh my Lord it was good. We generally split a steak between the DW and me. I generally cut the steak into pieces, separate the cap muscle from the NY Strip muscle, and keep track of which is which; I save the cap muscle for last (best for last). Well, when we had the prime steak, I was eating a piece of the NY Strip muscle, and I was bummed out that I had (I thought) accidentally eaten my piece of the cap muscle first. As it turns out, of course, it was the NY Strip muscle, and it was just that much better than a normal (Choice) NY Strip muscle. The cap muscle was out of this world. I should really just pony up the $20/lb for the Prime more often!