I think it's not true, J-20 may very well be for export, J-20 could also make it to a carrier. It's not set in stone. People just assumed because America did two jets and did it, China will follow the same perimeters.
My feeling is J-20 is the primary fighter for everything, J-31 may make it on the carrier, but the far more reasonable option is the J-20 IMO.
I think China is set on one, and looking at another. Recently some say plans for J-31 are finalized, but how true is it, and finalized to what is questionable.
A catapult carrier can defiantly launch J-20, America even considered F-22 at one point but opted for F-35.
J-31 and J-20 could just be two options, like F-18, F-16.
As to the latter part, well, we are all military enthusiasts, anyone who doesn't want it, wouldn't be on this forum.