I add one, Payment scheme.

All that you wrote is related. I'll give some illustration.

Let's say one big pool with big Hashing power and solving much block than other pools, and they have a lot of miners. That total solved block will be shared to their miners (to a lot of their miners) depends on miners contribution to the pool.

Another pool with less  Hashing power and solving less block than the 1st pool. That total solved block will be shared to their miners (fewer miners) depends on miners contribution to the pool.