they usually are part-time employees, particularly in places where the instructor is paid per class and not per person taking the class. As an independent contractor, the instructor MUST carry liability insurance..
They could be either.
Speaking tax-wise and legally (former CPA, not an attorney), to the extent that the business controls and reviews the performance of the worker, they’re more likely to be an employee. It’s a facts and circumstances test for tax purposes, so know how you want to structure the deal.