My 1988 edition also refers to Grades and I suspect that came from the original back in 1961.

AFAIK other branches of dance such as ballet, stage and tap use the term for their class descriptions and examinations.
Each dance organisation makes its own choice of which figures are included in which level, and how that level is described both for medal tests and for competitions, so the earlier advice to look at the figures is the best way to go.

Different levels are described in different ways for;

Teacher qualifications: Associate, Member/Licentiate, Fellow.
Medallists: Bronze, Silver, Gold, Gold Stars/Bars.
Classes: Beginners, Improvers, Hobbyist etc

Societies originally found it simple to base Bronze medals on the Associate syllabus etc but changes and developments have meant that the two do not now always align completely.