Car Charging Points

Yes.

Both will convert to DC and to the required voltage, but one on a nice big fat three-phase supply will charge much faster.

Tesla Superchargers are connected straight onto the 11kV grid...

It's very largely due to the technology of how power is generated ie with three sets of winding known as "phases".

ideally, all electrical consumption would be three phase also in order that the same power was drawn from each phase but on cost grounds, often only a single phase is installed. The hope being that by chance/design all be be equally loaded. However larger loads are three phase to prevent unbalanced use which causes all sorts of voltage related problems.

Fast electric car charging points are often around 60Kw and so invariably three phase. This also produces a smoother DC (less ripple).

The need for hundreds, even thousands, of these is one reason why mass electric car use would be impossible in the UK because they would be in use at times of the existing peak electrical load on the system.