All of them are embedded within Z2 advance tech.
For my use(mainly TV and ext speakers),
I use cast screen when i want to watch Youtube videos,from my Z2 to my Samsung Smart Tv(Internet-capable) by pressing the Cast button and it does not need to connect to same wifi network.
I use screen mirroring when viewing photos,small length videos and some songs to my TV. Its kinda easy if your device(TV in this case) is wifi direct capable or DLNA/Miracast certified,the response time between the action done on smartphone to the TV is relatively fast and without using a wifi network at all.
As in for throw,i use it to throw songs from my Z2 to external speakers or to my laptop's speakers.
However,a throw option is also available when to view photos and videos and it will auto-choose with sort of tech to use to "throw" the media.
For example,if you throw your picture to your TV,it will initiate Screen Mirroring.
If you throw a song to ext speakers,bluetooth instead is used.
Throw is by far the easiest way to enjoy content to other device but its the hardest to understand how it works. Screen mirroring only useable for ext displays. While Cast is somehow like you upload something into a TV temporarily to view them(Casting) instead of constantly real-time streaming of whats in your phone. Its particularly handy when you want to enjoy songs but you are low on battery.
I hope that will clarifies much as per your curiosity
-We are living the era with just so much tech, which are tech-nically difficult to understand hahaha