Redeem and Settle

Redeem

Suppose you have a neutral position (equal amount of long and short position). In that case, you can convert it back to the underlying collateral and take out your money before expiry.
For example, You minted 1 ETH option 1 month back and want to get back the 1 ETH, you can redeem it by having 1 long and 1 short position.

Settle

After expiration user can convert his long position or his short position back to the collateral. To settle your option after expiry you don't need a neutral position.
Settlement is done via Polynomial protocol for all the options, and the payout is distributed to all users. (Note: Settlement price for all option protocols will be the same after expiration if the strike, expiry, and option type are identical).

Payout for call option is given by:

$price(option)=max(price_e(collateral) - strikePrice,0) - Premium$
Note price(collateral) is the price of collateral at the expiry time.
Hence if the price is below strike price then the option is worth nothing.

Payout for put option is given by:

$price(option)=max(strikePrice - price_e(collateral) ,0) - Premium$
To get a more in-depth understanding of option payoff checkout the video above or read more in investopedia.