Q: iCloud Music Library - how does it work?

iCloud Music Library basically supports two Apple-provided services:

• iTunes Match
• Apple Music

It sounds as if you are not an iTunes Match subscriber.  I suspect you are also not interested in Apple Music, because you mention you have already purchased all your music.

Therefore, you should not use iCloud Music Library.

There is more information here:

iCloud Music Library: Understanding differences between Apple Music and iTunes Match - Apple Support

Anything you purchase starts off in iCloud (Apple has unfortunately decreased its vocabulary and tends to use a single term for what others in this world think of as different things ). If you are using an iCloud service such as Apple Music, and have it turned on, your personal music that is eligible gets a copy placed in iCloud (but it is always best to make sure you have a copy on your computer too, or at least on backup).  If a copy can be matched with something already in the iTunes Store then nothing gets transferred. If it is something they don't have a copy (possibly modified) will be uploaded to your user area on Apple's servers.

What is actually where only you can tell us because we can't see your computer.  You have to interpret the icons.

iTunes Match: Understanding the iCloud Status icons - https://support.apple.com/en-us/HT203564

iTunes 11 for Mac: Symbols used in iTunes - http://support.apple.com/kb/PH12106

There are many "places" in iCloud (a general term related to Apple's online presence).  Your iCloud Music Library is one place.  The iTunes Store (and its repository of media files) is another place.

Your iCloud Music Library is your personal iTunes music library in iCloud.  When you first start using it, iTunes either matches or uploads your songs (in your local iTunes music library) to create your iCloud Music Library (minus any ineligible items). 

If you do not have songs in your iTunes music library (you only show your iTunes Store purchases), my guess is that your iCloud Music Library does not have any songs.  Therefore, when you enable iCloud Music Library, you don't see any songs.  If you want those songs in your iCloud Music Library, download your purchases from iTunes Store.  iTunes then adds them to your iCloud Music Library.  You can do this with iCloud Music Library enabled, by going to the Purchased screen in iTunes.  Click on your name at the top of the iTunes window, and then Purchases.  On the Purchased screen, set it to show Music - Not in My Library.  Download previously purchased songs as desired.

Download your past purchases - Apple Support

It would be a good idea to keep a local copy of all of your purchased items.  You can download them again from the iTunes Store, but if the artist decides to pull an item (such as an album) from the iTunes Store, it will no longer be available for download.  The songs may also be in your iCloud Music Library, but what if an error causes your iCloud Music Library to be lost, or you fail to renew your subscription (or decide to cancel it).

Space Ranger wrote:

 

unfortunately thats where the confusion still in fact lays. because its auto enabled when I launch and sign into iTunes.

So make sure the iCloud Music Library is turned "off".

Here is how:

• In iTunes, go to iTunes > Preferences > General from iTunes' menu.  Make sure "Show Apple Music" is not checked.  Also make sure "iCloud Music Library" (if it appears) is not checked.
• Check Store > Apple Music from iTunes' menu.  Make sure there is no indication there that you are using Apple Music.

iTunes Match is the name of a subscription service Apple provides.  iCloud Music Library is a component of that service.

i remember iTunes match would have purchases in there as well downloaded or not.

Normally, it would, because those purchased songs are usually added (and downloaded) to your computer's iTunes library (which adds them to your iCloud Music Library).  It's not clear to me if you ever added them to your computer's (current) iTunes library, or if you are only seeing the songs (through their iTunes Store link) because they are past purchases (perhaps made from a different iTunes library before you had iTunes Match). 

The "concepts" are different.  iPhone is a mobile device, usually with minimal local storage.  Mac is a computing platform, usually with plenty of local storage.  The default functionality on each is optimized for the platform being served.  Also, it's not "redundant" for most users, because iCloud Music Library contains iTunes Store purchases AND songs added by the user from other sources (often more of the latter).  For you, it may be only iTunes Store purchases, but that's not the norm.  Therefore, showing your purchased songs is not the same as having an iCloud Music Library (for most users).

On a Mac, you need to add a song to your iTunes library in order for that song to appear in your iCloud Music Library (if it's not already there).  That makes perfect sense to me; I don't necessarily want every song I've ever purchased to be in my current music library.  I can also REMOVE a song, that I no longer want, from my iCloud Music Library.  It remains a purchased item that I can download again from iTunes Store, yet it no longer appears in my iCloud Music Library.  That's what you are describing; songs that are past purchases, but do not appear in your iCloud Music Library.

On an iPhone, you may want to play a purchased song, but not store it locally (to save storage space).  Not everyone has an iCloud Music Library, which is part of subscribing to iTunes Match and/or Apple Music, so Apple provides the option to stream purchased items as a benefit of buying from iTunes Store.  You can't stream other song you added to iTunes library from other sources (unless you have an iCloud Music Library).  You said you have your lCloud Music Library not enabled (on iPhone), so it's like you don't have one.