NO they are not like AMD, They operate as a Joint Venture(Co-own the fabs/dev/production). They use to go by Toshiba/Sandisk.
Toshiba transformed to Kioxia[2019] thanks to the Nuclear disaster in Japan.
WD bought SanDisk[2015] and has essentially re-branded everything to WD, the only part that remains are the part numbers (
SN850x).
Kioxia has been neglecting the consumer space outside of OEMs, Large presence in professional/server market pushing different EDSFF form factor. WD is inverse, mostly consumer facing + OEM, with barely any server/datacenter products.
Rumors of merging the companies have existed for awhile, There are similarities to the IMFlash(IMFT) Joint Venture Micron and Intel ran, although Kioxia doesn't have any other business so it would make more sense to me as a straight buyout from WD. The economics of co-development and manufacturing are more lucrative than doing independently. As such I would expect them either to continue in this partnership or for WD to attempt to buyout Kioxia as they appear to be the more successful partner with a more recognizable brand (Expensive marketing hit going from Toshiba to Kioxia). Also WD is working on emerging memory,
Kioxia statements on different memory techs have been negative (Maybe for good reason see end of Optane).
Compared to Hynix, Samsung, & Micron. Kioxia and WD are the ones to watch for disruption as neither is in the DRAM business and could see the most to gain by disrupting.