Wagyu is a broad term which literally means Japanese cattle.
While Kobe beef is the term which is used for beef actually raised
in the province of Kobe. There are other regulations that beef in
Kobe must follow in order to be certified Kobe beef. Wagyu can be
raised anywhere in the world and still use the term Wagyu.
Both Kobe and Wagyu are well marbled beef but Wagyu a bit less
so and is priced less expensively.