You are right that the initial 4 number block encodes the status.
So when climbing from Blue, through FQT to SEN, we get three sets of numbers.
When I finally got the M&M VISA card four years ago, I was given a new number - the CC number naturally - again.
I wrote to customer sevice as I wanted to have a SEN number that was not a credit card number for obvious security reasons.
Hence I was awarded an OS SEN card with my old SEN number on it. It is really cute and looks so much more inncent than the LH card. For reasons of curiosity induced stupidity, I alternately check in with one or the oher and the miles always end up on the same account.
So as the other posters say, it is one monolithic system.