Yes - you pay and they decide later what you get.

Max speed to 5GB per month after which they reserve the right to slow down your connection.

I guess that means all our plans here in New Zealand are technically "unlimited"...

You know, the ones that give you X GB of traffic, after which you're throttled back to dial-up speeds.

That sounds like a mobile plan in the €30 per month range, not like an unlimited residential plan.

Can you then explain the use of the term "unlimited"

The carrier has an unlimited license to distort the English language.