Even according to English Wikipedia: https://en.wikipedia.org/wiki/Flat_rate
"A flat fee, also referred to as a flat rate or a linear rate, refers to a pricing structure that charges a single fixed fee for a service, regardless of usage."
Emphasis mine. I'd understand this as there being a service (e.g. high-speed DSL) which you pay a fixed fee for, independent of how much you use it. That does also mean that if you use it more they don't shut it off, because otherwise you're not getting the service independent of usage.
In the 90s, when the Internet started to come into popularity, me and friends were desperately trying to get a connection that didn't cost money per time unit.
For the longest time, with no free local calls like the US had, that simply did not exist, at least via dialup. One option was a "Standleitung", which was almost literally a permanent landline between you and your provider, same signaling and all. Only small providers would usually be talked into it, but then you had to pay a (at the time) huge monthly fee to the Post/Telekom because the line took resources away permanently. Some few people were lucky enough to be able to establish radio channels with their provider (this was long before WiFi was a thing). At one of my first jobs, I got ISDN "callback" as a benefit, which meant that I could call the router, hang up immediately, the router would call back and establish the connection, company would pay!
Finally, after what seemed like an eternity, the first few flatrates appeared. Stay online as long as you want, download as much as you want (at speeds that were still measured in kilobytes/second, but completely adequate for the time). It was definitely Unlimited.
Finally, I remember the “Alkohol-Flatrates” that came up in clubs a few years later (and were, unsurprisingly, soon outlawed). Their point was that you could get a theoretically unlimited amount of drinks for your cover charge of typically 15DM or so. In practice that’s a stupid idea of course. I tried it once at the behest of a coworker: The drinks were atrocious, the floor was covered in a thick grime of “free drinks” and the crowd consisted of the type of people who would be attracted to an “alcohol flatrate” in the first place.
My German O2 plan is called a "flatrate" and is throttled after 300GB according to their "fair use" policy. Both terms are verbatim what O2 calls it, Germans have a lot of anglicisms. They claim it has "bis zu" 50Mbit/s ("bis zu" meaning "up to").
So sadly no, in Germany Ginger Beer is called Ginger Brew, but DSL contracts are still scammy.