Wagyu vs American Wagyu
According to the American Wagyu Association, most Wagyu beef are bred with Angus cattle in the United States. Thus Wagyu in America are half-blood. There are full-blood cattle, but most of the full-bloods are used for breeding, not for eating purposes since the numbers of full-bloods are very limited.
The Association was initiated in Texas on March 14, 1990. Since then, it promotes Wagyu into American and Canadian markets and controls the registration of Wagyu mainly in those countries.
Even if it is an American Wagyu or a half-blood, as long as they are one of those four breeds, they would be called and registered as Wagyu.
However, you may notice that some specific prefectures’ (like Kagoshima and Miyazaki) names, grading for the meat such as A5, or a specific name of the brand are written on the menus in restaurants, implying that the Wagyu is imported from Japan. Moreover, those imported ones are considered as the more premium ones -- they have passed the strict tests.
For example, “American Kobe” does not exist. That is the same thing as saying “Japanese California”, which makes no sense. Kobe is used as a marketing term; Kobe “style” implies that they are not authentic Wagyu. It is the same how American Champagne cannot exist. All sparkling wine cannot be called Champagne, which are produced in a specific area in France and meet the highest standards -- just like Wagyu.
Difference
The biggest difference between American Wagyu and Japanese Wagyu, aside from the wider rating system and diverging cattle-farming techniques, is that Japanese Wagyu is purebred, whereas American Wagyu is crossbred. Authentic Japanese Wagyu beef is sourced from specific breeds, the most common of which is Japanese Black (Kuroge), and the lineage of each cow is traced to ensure pure bloodline.
As the world's interest in Japanese Wagyu beef grew, American cattle breeders sought a means to transfer some characteristics of real Wagyu into domestic meat.
This resulted in the development of American Wagyu cattle, which are crosses of Japanese and Black Angus cattle. American Wagyu will still be extremely marbled with intense flavor, but it's most likely Wagyu bred with Angus.
The Angus beef crossbred with Wagyu in an uncontrolled, unregulated, and undefined amount of DNA. As a result, American Wagyu does not have the sweet umami flavor of Japanese Wagyu and never reaches the same melt-in-your-mouth level of marbling. Not that American Wagyu isn't tasty.
With Japanese Wagyu being so fatty and flavorful, most individuals can only consume a few bites before being overwhelmed. So, if you're in the mood for a steak meal and want a giant steak, you probably will not get it with Japanese Wagyu.
The American Wagyu is still fantastic. You can eat more of it if you want to. The typical beefy flavor of an Angus steak is present in American Wagyu. The Japanese Wagyu just doesn't have as much of that beefy flavor, and then there's that umami flavor that's difficult to describe. It’s almost like sweetness.
If you have the opportunity to try one of each, you will learn something new and appreciate it for more than just being so pricey. "Try several kinds of Wagyu from different countries and compare those."