Most streaming services don't have a downloading function as the whole point of streaming is to play NOW. What you may store is a playlist locally via that service's app, though it's not the actual files.
I subscribe to Tidal Hi-Fi and they do allow downloading certain files, just the ones artists have approved and just in the common 320kbps form rather than the 16bit/44.1 FLAC files you get with the "Hi-Fi" subscription. Most of my use of the Tidal Hi-Fi service is streamed through my Bluesound Vault, where I also have my own small library of digital files stored. For me that's about 300 CD's and a few FLAC files in 24/96 that I've bought and downloaded.
For me, the Bluesound Vault is ideal because my computer is OFF while I'm listening to music. That's good because it's in a different room (my office) than my system (living room) and the Vault make zero noise. Having both Tidal Hi-Fi and my files under the control of a single app on my tablet is great.