Mini and Nano (in regards to P2Pool) are separate Mining pools. Think of them as a very big miner. The bigger the miner (i.e. more hashrate) the time to hit a block is lower and therefore he receives more rewards per time interval. The smaller pools (Mini/Nano) are for people with low hashrate devices so that the blockreward gets split somewhat equally between them.
For example if you would mine with a very low hashrate on your own, you'd maybe hit a block every 10 years. If you then combine your hashrate with other miners, that have a comparatively high hashrate to yours, the pool hits blocks much more often, but you won't get rewarded that often because you didn't participate that much. If you then join a pool with people with low hashrates, your mining pools hits blocks more often than you would by yourself, but not all too often. But it's also much more likely for you to get rewarded a piece of the block reward, as you contributed somewhat equally to the pool.
I hope this explanation helps with your understanding and I didn't butcher to many details ๐