Streaming rates with Apple matched music held on Apple servers versus locally stored files?

I use Apple Match to synchronise my music library between different devices. I do not subscribe to Apple Music. My original files are stored in ALAC on my Mac and I use iOS's Remote app to stream the music to a number of AppleTV3s I have connected to external DACs over Airplay. I'd like to know what the bitrate is when I do this (with the local lossless) files. Is it still lossless or are files transcoded to 256K AAC? Also, what happens if I 'cast' the same music to a specific AppleTV using the Music app and Airplay? Is it also held at 256K AAC? I confess that I can't really hear the difference between lossless and AAC in my system, so my queries are probably moot, but I'm interested in the technical aspects nonetheless. Thanks in advance.