Adjusting sizing after trying on a 32DDD

First, this sub has been an incredible resource and I’m so glad it exists! I did the A Bra that Fits calculator and I ended up being sized as a 32DDD. I ordered a bra from Soma and the cups fit well but the band was too tight - I think I need to go up to a 34. I know that my cup size might then be different than DDD. Do I need to be looking for a 34DD, or a D? If someone can explain how the sizing ratios works, that would be amazing!