Ok, you are right, there are different versions J-15D. But given the inevitably low total production of the J-15D, I strongly doubt that the Chinese Navy would be willing to differentiate between the different versions in actual operations. Maybe continue to observe…
No, it's not that "there are different versions of J-15D".
Right now, there is only one variant of J-15D which is confirmed -- it is STOBAR compatible only. It may have entered production in small numbers.
In the future, we should expect a CATOBAR compatible variant of J-15D to emerge, as we are seeing its mockup on CV-18. A potential future CATOBAR J-15D variant will likely aim to be compatible with both CATOBAR and STOBAR carriers, and likely succeed the current small number of J-15Ds in production and service.