Hmmm, beantwortest Du Deine Fragen immer selbst? ;o)

"Toilet bowl" wäre die Toiletten-Schüssel, analog könnte man "loo bowl" sagen - Es gibt aber nur 57 Hits in Google ggü. knapp 4000 für den von Dir erfragten Begriff - ich würde daher bei "toilet bowl" bleiben.

Btw. wieso ist das in der Domain "agr." angesiedelt?

'Toilet bowl' is the only choice in AE. However, 'pan' seems to be used in BE ('lavatory pan,' 'toilet pan,' 'loo pan'), I'm not sure how exclusively. Apparently in some older British toilets the bowl was made of metal, not porcelain; whereas in the US, metal toilets are rarely seen except on trains.

...or it could also be that British toilets sometimes have a flatter shape.

Is it possible that the BE "pan" has a similar meaning or origin as the German "(Bett-)Pfanne"?
:-)