There isn't any single global ratings board for hotels that has any legal definitions associated with it.

In some countries, a national or regional hotel board may have specific definitions.

I seem to recall being in a few countries where "First Class" did not equate to the top level of quality. It was a tricky term...something like "Luxury" might be top and "First Class" second.

Star ratings are equally difficult. Forbes in North America is pretty tight with their fourth and fifth stars. A very good Ritz or St. Regis type hotel might be a four-star. Some smaller countries are quite a bit looser - the local hotel board may award five stars based on amenities and quality that would align more with a mainline Marriott or Hilton in North America. Some countries regulate the hotel ratings from a government perspective...obviously someone like Forbes creates its own standards.