Greetings TitansOXD,
Thanks for using the Apple Support Communities.
I see that you would like to know the difference between saving an album and downloading an album to your Library. It's important to make sure that you know the difference between the two, so I'll be happy to help assist you with this.
Please see support article:
Add and download music, shows, and movies from the Apple Music catalog
, specifically:
When you add content to your Library, you can access it across all of your other devices, as long as you're signed in to all of your devices with the same Apple ID.
You can also download content to your iOS device or computer so that you can listen to or watch it when you're not connected to the Internet. You must download the content to each device that you want to use for offline listening.
There's no cost to add or download content. Learn more about Apple Music and how to join. If you're not a member of Apple Music or want to purchase an individual song or album, you can buy it from the iTunes Store app or in iTunes on a Mac or PC.
Only when you download music to your device to listen to offline is when it will take up space.
Let me know if you have any questions.
Have an amazing day!