Right on indy master. Ted Turner bought JCP and renamed it to World Championship Wrestling, which was the name of the show on TBS.
The lineage of the NWA and WCW titles intertwined, when WCW started acknowledging Flair as their WCW champion, while Flair was still the NWA champion. The Big Gold Belt represented both titles. In what was a confusing time, Flair dropped the NWA title to Tatsumi Fujinama at the Japan Supershow, but WCW continued to recognize Flair as "WCW champion". Flair would eventually win back the "NWA" title and they were once again merged.
When Flair ran off to the WWF with the Big Gold Belt, both organizations stripped Flair of their titles. WCW introduced a new design for their "WCW" champion. The NWA eventually settled with Flair over this deposit and crowned an NWA champion, using the Big Gold Belt to represent them. This is where the two belts became distinguished.
WCW succeeded from the NWA after the NWA tried throwing their weight around with whom to book to win the NWA title. There was disagreement and WCW cut ties renaming the Big Gold Belt to the WCW International Title. Flair eventually won this belt and then unified it with the WCW title, making, once again, the Big Gold Belt the WCW title.
The NWA never had a presence on WCW television at this point and Vince purchased WCW, not the NWA, since the NWA continued to exist (barely) on it's own to this very day.
That is how Shane Douglas was able to win an NWA title tournament and then throw down the belt, since the NWA was on it's own. Also don't forget that the NWA briefly appeared as a faction in the WWF in the late 90's with Jeff Jarrett as it's North American champion.