well mining is creating new coins which is made through the GPUs or ASIC ( advanced something somthing circuit... just google it) create huge amount of hash (low end can create like 10-100 Mega Hash, ASIC can be a few tera-hash) that helps secure the blockchain. The first hash that meets the difficulty requirement will be selected and the miners are awarded ( at the moment is 25BTC but the halving is coming soon!!!). Pools are just like huge miners which receive the hashes from individual and find the one who can meets the difficulty requirement. However pools still award for miners who certain difficulty like 1, 2, 100, 1000, 1 million or more. The amount of bitcoin you receive equals to proportion of share you submitted. For example, your share got the difficulty of 1 then you got 1 share, your share got the difficulty is 500 then you got 500 shares. Your amount of shares in 1 round is divided for the total shares of the pool is your proportion (PROP system). When your pool finds a block ( which means someone submitted a share that meets the requirement), the round will end ( I think so) and the pool will receive 25BTC and share the amount with the miners. For example if your proportion is 1% you will receive 0.25 BTC. However it depends on the system like PPS ( pay per share) PROP ( proportion system like in my example), PPLNS ( pay per last n share - just google not really understand it LOL). If you are a solo miners ( without pool) and you find a block, you will receive 25 BTC on your own.
Faucet just like its name, is all about dripping
. You will earn various amount of BTC but is really really small like 100 satoshis to 100000 satoshis ( depends on how rich the faucet is) by solving a captcha and receive it through faucetbox account, micro something I don't remember or xapo wallet but maybe it is through accumulating to some amount ( usuall 5500 satoshis).
Hope this will help you my friend! Good luck