Neither are required. If you operate as a sole proprietor, you use you Tax ID number (Your social security number). If you want to set up a partnership or a corporation to run your business, then you must obtain a Tax ID (EIN) from the IRS. It's a sim pie process.
AirBnB collects the tax and includes it in your payout. You receive a quarterly tax form from the town which you fill out and submit the collected tax to the town. It's just a pass through. On you federal and state taxes it becomes an expense.