Confusion isn't helped by the industry having picked "Fast" to mean "damn slow" and "Rapid" to mean "Normally moderately fast, but might not be; if it's DC it still qualifies as Rapid even so".
When I said "If using the type2 on a rapid" I was meaning the AC output on what is otherwise a "Rapid" charger with DC capability - usually the third hose, occasionally a type2 socket on a machine that has two DC hoses. I'm fairly sure this is what the OP was talking about.
These are usually 63A three-phase (so theoretically capable of 44kW), but Tesla vehicles can't use the full capacity on AC. For Model S/X plugged into such a supply you will get:
- 11kW (older car, single charger). Might go as high as 12kW if the voltage is high. Approx 33MPH.
- 22kW (older car, dual charger). Might go as high as 23-24kW if the voltage is high. Approx 66MPH.
- 11kW (facelift car, software locked, from early facelift production if 'upgraded charger' not paid for). Approx 33MPH.
- 16kW (facelift car, current production and earlier ones if you paid for the upgrade). Approx 48MPH.
At such a charger, you would do much better with the CHAdeMO adapter, giving a theoretical maximum of 48kW but more commonly around 40kW, so somewhere from twice as fast to four times as fast as using the AC.
Separately from 'Rapid' chargers, there are the so-called "fast" public chargepoints with type2 socket.
If you find one with 22kW capability (32A three-phase), then you will get the same numbers as above (ie. the car is still the limitation rather than the chargepoint). There are a moderate number of such points in the UK.
The majority of type2 chargepoints in the UK are 32A, single-phase (same as what most of us have at home), so will give 7kW to any UK-spec Model S/X (ie. the limitation is the chargepoint rather than the car).
You also occasionally find 16A single-phase, sometimes in the form of a post with two sockets that will give 32A to one car or 16A if both sockets are in use. That gives only 3.6kW, (11MPH).
Certainly when I've just found a Type-2-only post out in the wild I have only got 16AMPs, same as home ... 22MPH.
I think you are mis-remembering here. If you get 22MPH at home, that's almost certainly 32A single-phase = 7kW. That's also the most common thing to find at UK public chargepoints.
If you get 16A in the UK, it's almost always single phase and so only 11MPH.
On the continent (Netherlands especially), you may find type2 public posts with 16A three-phase, so give you 11kW, 33MPH (again, any variety of Model S/X can use the whole capacity). I've never seen one of those in the UK.
Tesla destination charging however comes in a wide variety of powers from 3kW up to 22kW, sometimes shared between multiple connectors, sometimes full power to each unit. These are type2 tethered cables (the same hardware as is sold for home installation, capable of being configured in many different ways).