Short answer, they typically pay in cash. Certainly for any small amount say 5K or less, cash would be the default payment method. Most casinos would probably cut you a check or wire money if you requested it Certainly for any large amount, they would.
Yes, online casinos do actually payout. Legal online casino apps and sites take the extra steps to ensure that all the available games are tested and audited for fairness so that every player stands an equal chance of winning.