No, as confusing as they are, I know them.
WWE Championship=Undisputed, WWF, WCW Championship
World Heavyweight Championship=Reintroduced after Smackdown got the exclusive rights to the WWE Undisputed Championship. The Undisputed Championship then was turned into the WWE championship and was based only on the WWE/F history. The World Title also has the history of the Old Hardcore, European, United States, and Intercontinental titles as they were all absorbed into each other at one point. Confidential did a piece on the World Heavyweight title and showed that its based on the history of WCW.
Basically as it stands right now(even though they changed their minds a million times), the WWE title is based on the history of WWE and the World title is based on the history of WCW.
Yeah, that's mostly true. The WHC doesn't have the IC and US lineage, though; it was made clear that both titles were 'brought back' and as such were de-unified with the WHC.