There were two fundamentally different proposals for concepts:
Indiana— concepts are records of signatures; checking is done "by signature"; an arbitrary mapping (adapter) can be defined. Notable authors: Doug Gregor, Jeremy Siek, Jaakko Jarvi, a lot of others I'm insulting by forgetting.
Texas— concepts are predicates of "actions" (usage of signatures; expressions). Notable authors: Bjarne Stroustrup, Gaby Dos Reis; later, Andy Sutton.
The crux of the issue is that Doug Gregor actually implemented the Indiana proposal (twice?) and Gaby never implemented the Texas proposal. By 2009, the Indiana proposal was well on track to being accepted; then ... it wasn't.
Fast forward 5 years, and now we've got a re-imagining of the Texas proposal, with no serious dissent, as all the Indiana folks moved on (out of exasperation, frustration; age; interest, whatever).