So what made it undisputed was that it was defended on both shows?
Do you not know what undisputed means?
Undisputed, in this sense, means that there is no question as to WHO the champion is.
for example, when there was an NWA champion, WCW champion, and WWF/E champion none of them could ever claim to be THE ONLY world champion.
For a real life example, take a boxer who wins the WBA, WBC, and IBF championship in the same weight class, he is usually regarded as THE UNDISPUTED champion because no one else can really claim to be the "best" at that weight division because this particular boxer holds every title and is THE BEST. period. no question.
in the WWE sense, when Chris Jericho beat Stone Cold and The Rock in the same night to win both the WWE championship and the WCW world heavyweight champion, the WWE called him the Undisputed champion because at the time, there were no other big name wrestling companies in the US, therefore, they regarded Jericho (and triple H and hogan and a few others after that) as undisputed champions because they were the holders of both belts. (it may have also been a dig at all the former people who ran WCW by eliminating their title) When Triple H defeated Jericho at Wrestlemania to win both belts, the next night on raw he brought the design show in this thread and they called it the "undisputed title" probably because Trips or someone thought it would be a good idea to have one belt and just call it the undisputed.
Now when the brand split happened, they couldn't really have 1 champion playing both shows and having him in multiple story lines with multiple competitors. Therefore there was a storyline to crown a new champion on Raw when Brock took the "undisputed title" to smackdown.
Eric Bishoff presented Triple H with the Raw title which was modeled after the old WCW title and given the name (and correct me if im wrong) "WWE World Heavyweight Championship"
When this happened, the belt that Brock was still holding over on Smackdown was renamed the "WWE Championship"
This was done because since there were two top champions and neither could claim to be "only the best"
Now, over the years, with all of the new drafts that happen from time to time, the Champions and thus the belts have switched from show to show. Currently as it stands, the World heavyweight title (modeled after the old WCW title) has been THE title on Smackdown while the "Spinner" (aka WWE Championship) has been on Raw.
When the Heavyweight title was on Raw it was considered more important than the WWE championship just because of the fact that it was the "World heavy weight title" and not just the "WWE championship" the world is bigger than the WWE.
however in recent years/months the Raw title has taken over in importance since its on the "main show"
and now with the ECW championship its even more convoluted. For their ever to be a Undisputed champion in the WWE again he would have to win the WWE championship (the Spinner) the World heavyweight championship (the WCW styled belt) and the ECW championship because then, at that point, no one else in any WWE owned promotion/show could claim to be the best since a single person would hold all three titles.
yes i know that was long, yes i know that was pointless, but i was bored and this ate up some time. Hopefully you learned a little bit and added a new word to your vocabulary.