For me, though, I'll typically use the word "outsourcing" to refer to contracting work to an outside party and "delegation" to refer to reassigning work to a coworker or colleague, especially to one who is lower on the company food chain than you.
Which is right for me?
It depends. If you have someone on your team who you trust and can train to do your given task capably, by all means delegate. If the tasks you need to delegate require a skill set or workload that your coworkers can't meet, then I recommend outsourcing.
For example, I work with some amazing men and women when it comes to editorial responsibilities, but none of us can code. Rather than dole out work that isn't in my team's wheelhouse, so to speak, I'll turn to a trusted contractor who can whip out tech-related tasks in no time.