Wagyu is the Japanese word for Japanese 和 Cow 牛. Over here it can mean anything, including Angus crossbreeds, but in Japan it has to be one of four varieties.
“Kobe” in Japan is a protected term, it’s extremely selective. Certified Kobe means that it has to come from Hyogo prefecture and be certified by an independent inspection board. Only 3,000 animals a year make the grade.
There is no protection in the US for the term “Kobe” so pretty much anything can be marked as Kobe beef here, including hot dogs (!).
Needless to say, genuine Kobe beef certified as such in Japan is exceedingly rare in the US. Imports have only been allowed since 2012 due to the mad cow scare.
Last time I checked there were only 9 restaurants that we’re licensed by the Kobe beef board in Japan. The list can be found here:
So most of the beef marketed in the US as “Kobe” is not Kobe as this term is understood in Japan. And CJ is right, there was a scandal about this a few years ago.