If you've signed up for Apple Music, then it can be even more confusing, since Apple Music also matches tracks the way iTunes Match does. Here's an overview of how these two services work in iTunes and on iOS, and how they work together.
Independent but complementary
On the membership section of the Apple Music website, Apple says that "Apple Music and iTunes Match are independent but complementary." They say little more, and when you look at the latest version of iTunes, it's not clear how iTunes Match works.
The first thing to understand is that Apple is no longer using the name "iTunes Match," at least within iTunes. iTunes Match is now part of the iCloud Music Library, which includes the following:
You may not have all of the above. If you don't have an iTunes Match subscription, and haven't signed up for an Apple Music free trial, then you iCloud Music Library will only contain purchased tracks, if any.
The iCloud Music Library, therefore, contains multitudes. To make sure you see these cloud-stored tracks in iTunes, choose iTunes > Preferences, click General, and check iCloud Music Library. On iOS, open Settings, and then choose Music > iCloud Music Library.
You can subscribe to either iTunes Match or Apple Music from the Account menu in iTunes. If you're already signed into these services, you won't see the iTunes Match and Apple Music menu items.
While iTunes Match and Apple Music seem to offer similar features via iCloud Music Library, there are some important differences. Here's how each one works.
iTunes Match
With an iTunes Match subscription, iTunes matches your library, uploads any unmatched tracks, and makes your music available on multiple devices through the iCloud Music Library. If you have low-quality tracks, iTunes Match "upgrades" them, allowing you to download 256 kbps AAC files without DRM. You can also download your files to any computer linked to your iTunes Match account, and listen to your music on any linked iOS device. iTunes Match has a limit of 25,000 tracks, not including iTunes Store purchases.
Apple Music
While the main feature of Apple Music is streaming from Apple's massive collection of music, Apple Music also matches your music library and uploads tracks that aren't in Apple's library. There is also a 25,000 track limit, as with iTunes Match, but Apple's Eddy Cue has said that this limit should be increased to 100,000 when iOS 9 is released. (It's not clear whether the increase will also affect iTunes Match, but it's likely that both services will get the boost.)
However, there is one essential difference between iTunes Match and Apple Music. While iTunes Match lets you download your music files and then play them anywhere, Apple Music adds DRM to your files. This means that if you rip a CD, and it's matched or uploaded to iCloud Music Library via Apple Music, and you download the files, say, on another Mac, you will only be able to play those files as long as your Apple Music subscription is active. If you delete your originals, or lose them, then you won't be able to access files without DRM. As such, it is essential that you keep backups of your original files if you use Apple Music.
If you have both an iTunes Match subscription ($25 per year) and an Apple Music membership ($10 per month), then you get files without DRM.
The problem is that Apple is not making a distinction between Apple Music files that you download for offline listening--this is a key feature of Apple Music--and files that belong to you, which are matched or uploaded. In addition, there seem to be bugs right now, causing many previous matched files to show as Apple Music files, and to contain DRM when downloaded, even for users with iTunes Match subscriptions.
Many users are seeing this problem with matched files showing as Apple Music files (with DRM), and this is presumably a bug that Apple will fix. But, for now, if you download any of these files, they will be locked with DRM, and you'll only be able to play them as long as you have an Apple Music subscription.
Which is best
The main issue is the integrity of your iTunes library. If you already have an iTunes Match subscription, I'd recommend you keep it, whether you plan to subscribe to Apple Music or not. If you want to continue using iTunes Match as such, it is now part of iCloud Music Library. If you also want to use Apple Music, that, too, is part of iCloud Music Library.
If you don't use iTunes Match, and only want to pay for Apple Music, then be aware that your original music files will have DRM added to them if you re-download them. Make sure you have a reliable backup of your library, just in case.