I'm not that poster but I'll answer:
Match: iTunes matches your collection, up to 25,000 songs, with ones in the iTunes store. What doesn't match is uploaded and is available on any Match-capable device. What is matched is also available on any Match-capable device and furthermore, the matched song can be downloaded to replace a lower-quality original file. You may keep these upgraded files forever.
Music: matches your collection (no mention of song limit) with the iTunes store. What doesn't match is uploaded for streaming and/or downloading on Music-capable devices. What is matched is just part of your collection. You can stream or download for offline use all of these tracks, but you may not keep any of them. Downloaded songs will be inaccessible and contained within the Music app, unlike Match songs, which, if downloaded, are stored on your hard drive like any other music files that iTunes accesses.
I get the confusion. Apple has done little to help this and it's very surprising that they've left it so murky.