I deleted my local music files

So I had been doing both of transferring my local music files to iTunes (on Windows) and listening to songs added from Apple Music catalog. What happened is I got a new Mac and wanted to free up some space on the Windows machine I had been using iTunes on (I now use both machines), and I decided to delete the local files. At that point I had my music files not only in the iTunes Media folder but also across other directories. I thought deleting those folders would not do anything to my library since they were all matched on cloud, but it turned out I cannot play the deleted local songs and I cannot download any of the songs in my library on either of my computers, even the songs I newly added. I find it odd that I can still download and play all those songs on my iPhone. So the question is would there be any way to restore those music with the songs from Apple Music? I never thought this would happen because I mean what is the difference between, say, adding a local music file to my library by matching it on iCloud Music Library, and adding that exact same song directly from Apple Music?