They're trying to piss you off. No really.
I think Bordeaux is pretty straight forward, you have 61 Cru Classé (Not "Grand Cru") sites, 5 of which are Premier Cru. This only applies to Medoc (And Haut-Brion in Graves / Pessac-Léognan). The rest are divided into second, third, fourth, fifth crus.
Then there's the Sauternes classification, where you have one Premier Grand Cru, Premier Crus below that.
St. Emillion also has a different classification, I won't get into that.
As for Burgundy, the land is so fragmented due to Napolitiantime laws of inheritance that the sites are incredibly small, and unlike Bordeaux they don't change much. As for classification of the very best wines that have their own AC it's like you said, ~560 Premier Crus, ~30 Grand Crus, that often just put their own name on the label, they're famous enough that you "should" know them.
The system is different, I think you just got hung up on the terms. Grand Cru in Bordeaux is either Chateau d'Yquem or St. Emillion wines.