Outsourcing refers to an organization contracting work out to a 3rd party, while off-shoring refers to getting work done in a different country, usually to leverage cost advantages.
It's possible to outsource work but not offshore it; for example, hiring an outside law firm to review contracts instead of maintaining an in-house staff of lawyers.
It is also possible to offshore work but not outsource it; for example, a Dell customer service center in India to serve American clients.
Offshore outsourcing is the practice of hiring a vendor to do the work offshore, usually to lower costs and take advantage of the vendor's expertise, economies of scale, and large and scalable labor pool.
