Most companies don't care whether your company has one employee (you) or a million. So it doesn't matter whether you call yourself a freelancer or a consultant

Most companies don't care whether your company has one employee (you) or a million. So it doesn't matter whether you call yourself a freelancer or a consultant or a contractor or anything else. What matters to them is whether the entity they will be contracting with is a person or a company. And as others have pointed out, this is usually for tax reasons: if the company contracts with an individual, the company is more likely to be viewed by the IRS (at least in the US) as your employer, and are thus subject to paying unemployment and payroll taxes.