Let's try this again... one vessel is mash/kettle the other vessel is lauter/whirlpool. In many startup sort of systems, only mash/kettle is fired. Dough-in in mash/kettle, do steps if desired, etc. transfer mash to lauter/whirlpool, sparge back into kettle. Start boil. Clean lauter/whirlpool. Run back into lauter/whirlpool for trub separation (and to free up mash/kettle), after whirlpool is done, run through heat exchanger... while simultaneously doughing-in your next batch in your hopefully rinsed out mash/kettle.
The vessels can't perform the same function. Only lauter/whirlpool has the false bottom/lauter pipes. Only mash/kettle has a mixer that can actually mix the mash around without forcing a bunch of debris/flour under the lautering mechanics. On cheaper systems, the lauter/whirlpool is insulated but not fired. Often there is a HLT under the lauter as well.
BUT it really depends on whose equipment it is because there are manufacturers that also do kettle/whirlpool designs. The lauter/whirlpool designs originated with the Germans... and that system design allows you to easily do decoctions, steps, etc.