The Thompson's books are divided by grade (first grade, second grade, etc.). Aside from that, I have encountered a pianist who says that he is considered to be an X grade pianist. What is this grading system exactly?
There are various grading systems used throughout the world. Grades are set by various music organizations and are designed to reflect the difficulty of playing a song, or the skill depth and breadth of a musician.
In Canada, I took lessons from teachers certified by the Royal Conservatory of Music and followed the RCM's grading system, complete with songbooks of graded songs and examinations. (I got my grade 8 piano before stopping lessons).
A frequently referenced grading resource is
McGrath, Jane. Pianist's Guide to Standard Teaching and Performance Literature. Alfred Music, 1995.
It is a fairly comprehensive list of piano (student) repertoire with each piece given a grade from 1 to 10, with 1 being the easiest and 10 being the entry point to concert literature.
The music foundations in various countries where developed to standarise music education. There are in most countries a couple of competing foundations. None you could consider canon.
In the US there has been a great reluctance to standarise education at a national level. If it is not expressily mentioned in the US constitution that an industry should be managed on a federal level then it is pretty assured it will not happen.
The idea of these foundations is not completely absent in the US. The AP music theory program exists to prepare candidates for college music. The later theory grades in other foundations form a similar role.