Whats the difference?
A relevant example to better understand the two:
Outsource=cut grass, weeding, landscape planning
You NEVER outsource your core competency but you can sub contract.
If for example you win a tender and your capacity to deliver is limited, you will need help. So you subcontract part of what you cannot manage. A subcon should be managed, watched closely, measured on performance and babied along the way, because what they bring to you should meet your stamp of approval. It ultimately helps you deliver on that tender you won.