Former Chef here from the great state of NJ: I have never been licensed. I've worked for some of the better restaurants in the state (including NYT 4 star reviewed and James Beard nominated chefs). I've never known a licensed chef.

The restaurants require licensing out the ass, and I know there are ABC (alcohol handling) certifications required for servers, but cooks don't. At least one person (typically a manager) needs to be ServSafe certified, but that's not a requirement for every worker.

Meanwhile, a hairdresser must be licensed before they can step into a salon and do work. My sister and wife both worked in the industry, and I promise you they would both scoff at the idea of a 1 hour form/test for someone cutting hair. There's a ton of hygiene related things that they need to know to prevent disease transmission from cutting and handling hair daily.

Whether or not you need a food handler's card is likely state-specific.