Your right for the most part on the grade A and B, but more to it. Yes grade A is more the fluid milk, grade B cheaper and for cheese etc but it is actually a little more complex than that and doesn't make much sense other than driving the price down for the farmer giving the dairy plants cheaper priced milk. Does make sense in a way dirtier milk, farmers that do not make sure they have a clean process get punished for the bacteria in their milk with lower pay, gives a incentive to do better. We are a grade A milk plant that makes cottage cheese and sour cream. What makes us grade A and we take grade A and B milk, is we check for bacteria every load. State only requires antibiotic test, all dairy is antibiotic free and checking for antibiotics is the only state requirement (reason is some people allergic can kill them).
We can actually take in grade B, test it, run it through our pump load it on another trailer, magically becomes grade A sold to another plant

I test thousands of loads a yr and it is very rare to ever see any 'bugs' in the milk, like mostly never. Been several yrs since I've rejected milk for bacteria.
Blah blah blah sometimes I talk too much