Two legal categories of worker with very different consequences for taxes, overtime and liability - and a label in a contract does not settle which one applies.
Whether a worker is an employee or an independent contractor decides who withholds and pays employment taxes, whether minimum wage and overtime rules apply, who is liable when the worker injures someone, and whether the worker is covered by unemployment insurance and workers' compensation. The classification is made by law, on the facts of the working relationship. Calling someone a contractor in a written agreement, paying them on an invoice, or issuing a Form 1099 does not make them one.
There is no single test. Federal tax law asks who has the right to control how the work is done. The federal wage-and-hour law asks whether the worker is, as a matter of economic reality, in business for themselves or dependent on the hiring business. A number of states apply a stricter presumption of employment for some purposes, under which the business must prove that the worker is free from its control, does work outside the business's usual line, and has an independent business of their own. The same person can be a contractor under one of these tests and an employee under another.
Misclassification is the reason the distinction has teeth. A business that treats employees as contractors can be liable for unpaid employment taxes, back overtime, benefits and penalties, and the exposure typically surfaces through an audit or a claim by one worker that then extends to everyone in the same role.
The question to bring a lawyer is not "can I call this person a contractor" but "which tests apply to my business in my state, and does this working relationship actually pass them". The answer is often different for tax, for wage law and for workers' compensation, and a business that relies on the label alone usually finds out which test it failed from an agency rather than from its own counsel.
Choose your state. Each link opens the directory page for the city in that state with the most currently published law firms in this practice area; a +n beside the city is how many other cities in the state also have one. The list is generated when this page loads, so a state whose listings have lapsed drops out rather than becoming a dead link.