For someone who relocated to the U.S. and whose native language is not English, I should not get involved in that discussion, but.....
In the U.S., a "sill cover" is on top of the door sill, under the door. In case of our Pagoda, it would be the "rubber mat".
The metal planking on the outside is commonly called "rocker panel" by bodywork types.
A "rocker cover" in most cases is also a "valve cover", like in the U.K.