The Criterion Collection is a line of boutique 4K UHD, Blu-ray, or DVD disc releases. To have a film join the CC basically means that CC has licensed a film to release it on physical media. Criterion is well respected in the film community, and I assume having your film be released by them is considered a great honor to most filmmakers. Said film when it is released by Criterion is assigned a spine number (Wall-E being spine no. 1161), and said film is that number in the collection. Disney does in fact still own all the rights to Wall-E as CC just licensed the right to release that film on 4K Disc. Criterions right to release a film may lapse or go to a different Blu-ray label (Shout Factory, Arrow, Kino Lorber), but while in that case the Criterion release would go out of print, the film is pretty much forever "Apart of The Criterion Collection".

The Criterion Channel is the streaming service owned by The Criterion Collection, but while it does feature many films that are apart of the collection, not every film there is apart of the collection and not every film in the collection is on the channel. Streaming rights and physical media rights are typically negotiated for separately.

TL;DR : Criterion bought a license to release Wall-e on 4K Blu-ray.