How is Gonzalo, the old courtier, different from the other courtiers in his reaction to the furious storm at the sea?

Gonzalo, the "honest old counsellor," keeps a level head while the other courtiers are panicking from fear of drowning in the storm. Therefore, he doesn't interfere with the ability of the crew to fight the storm. Gonzalo, who is always the optimist, is sure that "good Fate" will protect the people on board the ship; He knows that somehow all will turn out well.
Gonzalo is the opposite of the corrupt courtiers on the ship. He has a moral compass and isn't obsessed with saving his own skin or advancing his own career. His ability to see a bigger picture beyond narrowly focusing on himself allows him to keep calm in the storm. He is a loyal courtier, and in the past, he helped make sure that Prospero had not only food and supplies for survival when put out to sea, but books to keep him company.
Shakespeare shows that who we are as people shines through in how we react to adverse events.

Gonzalo is a wise old man who is experienced in the ways of the world. He's generally sympathetic to Prospero's claims to the throne and so stands apart from the other VIP guests on this tempestuous voyage. He's also separated from his fellow passengers by his reaction to the violent storm that Prospero's whipped up specially for them. Whereas Antonio and Sebastian are scared out of their wits, Gonzalo manages to keep a cool head. As the waves rise, and the storm brutally lashes the ship, he finds time to indulge in a spot of gallows humor, reckoning that the impertinent boatswain has the look of someone who will one day be hanged. In other words, Gonzalo figures that if the boatswain will eventually die on the end of a noose, that means he won't suffer death by drowning, and if he won't suffer death by drowning, then the ship won't sink, however desperate the current situation might be.