Mediocrity in grammar and branding, mediocrity in sustainable outsourcing.
Some wannabe-clever guy invented the term ‘out-tasking’ a long time ago, to mean a kind of outsourcing that involves only individual tasks and not entire processes (comprised of a series of tasks). You know, instead of taking all inbound calls and resolving tech support tickets and managing the workload of the call center, you just pick up the phone (not even greet the caller)—end of task. Sometimes it's helpful.
In any case, it's at best a grammatically inconsistent term.
The term to compare it with (and with which it should be consistent) is outsourcing: getting outside sources.
Meanwhile, ‘out-tasking’ is sending out a task (to outside sources of labor), not (the hiring company) getting outside tasks.
You don't call contact-center outsourcing ‘out-phoning.’ Or finance and accounting outsourcing ‘out-bookkeeping.’
Or hiring an entertainment agency ‘out-performing.’ (Internal managers are capable of the 'out-performing' themselves, with their daily bungling comedic routines. Such a riot.)
Nor is ‘outbound’ some sort of 50 Shades of Grey outsourcing.
‘Out-tasking’ is not a smart term, but as is expected in the idiocracy of business, it enjoyed a minor success, persisting for about a couple of years in a few mediocre circles.
On a related note, there was a wildly successful concept once called labor arbitrage, until automation, good taste, and decency outperformed it. But it still persists in a few mediocre outsourcing circles.