I thought a thicknesser was a sandpaper based tool that took off 1/32"
or so at a time while a planer was more for turning rough or too thick
stock into a finished board, 1/8" at a time using rotating knives. The
former did finished work while the latter's output needed sanding to
finish it. It looks like they both mean a planer though, at least in
the UK. Good question, sorry I couldn't help.

Jim