Every independent contractor is a business owner. You run a business even if you are your only employee and you don't have a company name. There are significant differences, however, between a business that's just you as an independent contractor and running a company with employees and a registered name.
If you're an employee, your boss tells you what to do and when and how to do it. The company also decides financial details, such as how you get paid and whether your expenses are reimbursed. If you're an independent contractor, your client tells you what he wants done but you decide, within limits, how to accomplish the task and you can negotiate the financial terms. The IRS says there's no single factor that identifies an independent contractor -- it's determined by adding up all the details of your relationship with your clients.
If you're a one-person shop doing business under your own name -- Jenny Smith, Plumber, for instance -- you own a business as a sole proprietorship. All the profits from your business are personal income, reported using IRS Schedule C and a 1040 form. Your Social Security number is the tax identification number for your business. If you us a business name such as Amazing Plumbing, you're still an independent contractor. You will, however, have to take added steps such as registering your business name with your county.
As an independent contractor, you can also form a limited liability company or a corporation instead of a sole proprietorship. If you go into business with someone else, a partnership is another option. If you incorporate, legally your company is now the independent contractor, even if you own the business. When clients hire your services, what they're really doing is hiring your corporation, which sends you out to do the job. In a sense, you've become you're own employee.
Having employees doesn't make you any less of an independent contractor, whether you're a sole proprietor or a corporation. It will, however, change your business. Once you have employees, you need a separate tax identification number for your business, even if you're a sole proprietor. You also assume responsibility for withholding their Social Security and income taxes from their paychecks. You can also hire independent contractors to work for you, but you get into legal trouble if you class employees as contractors.