That's outsourcing for the employer, but consulting for the employee. If I consult for a US company while being in South America, I'm still a consultant. They are the ones outsourcing.
A consultant is an advisor, that should have some specific technical or domain knowledge to advise people with.
In reality, everyone can call themself a consultant and i bet you can charge better money calling yourself consultant, even if you don't possess any specific knowledge and just work as a regular dev.
No, there are non-US companies that sell consulting services to US companies. If you are employed by one of these companies, you work as a consultant for a US company (usually as part of a team with several compatriots), and you are not a freelancer since you are employed by your company. If the contract finishes and you're left without a project, you're still employed and drawing a paycheck, and it's your company that finds you a new project to work on.
