For most grading systems the primary determinant of beef quality degree is based on the Ribeye.
Beef quality grading varies by country. In the US, for example, we follow the USDA grading which are USDA Prime, USDA Choice, USDA Select, while other countries use letters, numbers, or a combination.
Generally, restaurants, supermarkets, and butcher shops tend to mix-and-match these grades but it often confuses more than it helps.
On a global scale, the predominant grading systems are the ones used in the US, the Japanese, and the Australian.