They haven't clarified on how they'll do it but I certainly hope and expect that when a new build is pushed to the alpha players the anyone in the beta can still continue playing the last build they got. The whole idea (besides the sales pitch) for releasing builds to the alpha people first is so that they can catch the broken builds so they don't affect the larger beta. If the beta isn't playable when a new build is pushed, well, then it's affected, broken build or not.
Premium and Standard beta are periods of development, similar to alpha and beta. When the alpha is over and we move in to beta people who paid for premium beta will get access. People who paid for standard beta will get access at a later point. We do not know how long the premium beta period will last.
As for content differences, we don't really know. We don't know what's in the premium beta. That said, I very much doubt that the premium beta would show up with most ships and assets or even features in place, instead we'll see more and more get implemented over time. Standard beta being at a later point would thus be closer to the final game.