Actually, Warrants were part of the British Navy long before the Continental Navy. They were the Gunner, Sail Maker, Cooper, Bosun, Cook and Master. They were permanent ship's company and stayed with the ship even when it was paid off and laid up in ordinary. They had a lifetime appointment and they were allowed to have their wives and kids live on board when laid up and depending on the Captain, even when at sea. The Warrants could apply or be promoted into bigger ships but they could stay where they were if they were happy. They promoted from the lower deck after years of service.
The Continental Navy basically took the Royal Navy as it's starting point and for the most part did things the same way. A little less discipline but the same structure.