I think class is strength of recharge and rating is amount of charges. But I could be wrong/there might be much more
The larger numbered shield cells do come with more charges, and the B shield cells also have more charges.
D1 has 4, C1 has 5, B1 has 6, A1 has 4
D3 has 6, C3 has 8, B3 has 10 and A3 has 6.
I'm sure it will be similar for larger ones.