Under Adaptive Issuance, the staking power (weight of staked tez) counts double when calculating baking rights, compared to the delegating power (weight of delegated tez). Baking rewards cause increase of tez supply (inflation), so it is correct that weight of staked tez counts double as weight of delegated tez.
Assume your chain has 1,200 tez supply, out of which 600 tez is staked and 400 tez is delegated.
At every cycle, the protocol has a bucket of baking rights to distribute to bakers. The process is as follows:
First, it takes 2/3 of the baking rights and distributes them based on the distribution of the 600 tez of stake amongst bakers: the more staking power, the more rights.
Then it takes the remaining 1/3 of baking rights and distributes them based on who these 400 tez are delegated to: the more delegating power, the more rights.
The combination of staking power and delegating power is known as baking power.
Then, assuming the baker is working properly, they will bake and attest when it's their turn, and get rewarded for that.
(this is simplified: in reality, rights distribution is a pseudo-random function weighed by the rules above; you also have attestation (endorsement) rights distributed the same way; and there are global limits enforced. if you go over the limits, you are overdelegated/overstaked and your power is capped)
The protocol automatically distributes stakers their fair share of rewards (based on how much they contributed to the baker's stake). As far as delegators are concerned, the baker is expected to transfer them their share using TRD, TezPay or TAPS.
Baking power determines how rewards are distributed within a cycle. But how much is being distributed overall? This depends on the global amount of staked tez in comparison with the total supply, as well as a variable rate. This is recalculated at every cycle, and capped between 0.05% and 5% annually. Roughly speaking, the more people stake, the less the rewards will be.
Important note: the baking power of the entire tezos network consists of 2/3 staking power and 1/3 delegating power. But this is not true for an individual baker! Indeed, a solo baker who staked their entire balance and has no delegators has a delegating power of zero, and their baking power comes exclusively from staking.