On a normal faucet, you will enter your wallet address, solve a captcha and be rewarded with Satoshi instantly. More often than not you will get a pop-up screen or a 2nd captcha to solve before you can get the payout. Most payout in 0 to 15 minutes some as long as a day.
Some of these faucets require you to build up to a certain amount of Satoshi in order to get a payout instead of instant, you should check these out before committing a week’s worth of work only to find out they are inactive. (FaucetHUB chat is a good place)
On a miner page, you will enter your wallet address, start the miner and just leave it going. It will earn for you as long as it is running. Miners payout at specific thresholds or times. (FaucetHUB, for example, pays out at 100 accumulated Satoshi)
Floodgates and auto faucets are similar to faucets except you only need to solve captcha or pop-ups once and as long as you have the page running do not need to solve them again. Most payout in 1 to 10 minutes.
People who run the websites are usually compensated for payouts by ad revenue. Most of the sign-up and verification is for anti-fraud. (so bots don’t drain their accounts) If the faucet is constantly out of money or has errors, move on.