With call options, the buyer hopes to profit by buying stocks for less than their rising value. The seller hopes to profit through stock prices declining, or rising less than the fee paid by the buyer for creating a call option. In this scenario, the buyer will not exercise their right to buy, and the seller can keep the paid premium.
With put options, the buyer hopes that the put option will expire with the stock price above the strike price, as the stock does not trade hands and they profit from the premium paid for the put option. Sellers profit if the stock price falls below the strike price.