After 9 months flying in NA I can honestly say most non-standard items are instigated by ATC. Most places don't even have an "Approach" freg only director-arrivals etc.
They don't call it
approach control because they drop the first part for abbreviation. It's customary in British English to drop the first part (so they say
control) and the opposite in American English, so in American English having dropped the second part they say
approach, but it's the same thing in both cases when referred to in writing.That's why Americans call the
Final approach, Final the British types call it
Approach. But they're both referring to exactly the same thing.