Peter Duncanson [BrE]:

"chainwheel" is used by the British company Brompton Bicycle Ltd.

Indeed, a reputable firm, but still only one example.

It is used to refer to the whole "wheel" to which the pedals are
attached. The "chainring" is the replaceable outer part of the assembly.

Confusingly, they - the supplier quoted below, that is - appear to be
using both "chainwheel" and "chainring" to refer to the same thing, the
cog itself. The unit comprising the cog and cranks (to which the pedals
are attached) is called a "chainset" or, as they call it, "crank[ ]set".
(I'll give them that: "crankset" is a reasonably common variant of
"chainset".)

For instance:
http://brilliantbikes.co.uk/brompton...hainwheel.html

44T Brompton BLACK edition crank set (left and right complete) - the
Brompton "spider" crankset
....
This is the BLACK edition crankset - with black chainwheel and
cranks
....
The "spider" crankset has a few advantages over the older fixed
crankset:
The chainring protector is held on with screws rather than plastic
lugs so is less liable to falling off
The chainring can be changed without the need to replace the crank
as well (making it easier to change gear ratio)

I've no doubt "chainwheel" is used in the UK (to refer to individual
cogs), but it's not the usual term, and I still think it's rare. All the
major suppliers, such as Chain Reaction Cycles or Wiggle, will use the
term "chainring". Even the supplier above does, on their website's menu.

--
John