When I cast a YouTube video from my phone to my Roku it's not actually streaming the video over WiFi from my phone to the Roku but rather instructing the YouTune app on Roku what to play. I.e. if I power off my phone or leave WiFi coverage the video will keep playing.

I'm thinking of getting a Chromecast particularly for playing music from my Google Play Music subscription (there's no Google Play Music app for Roku ).

Can anyone confirm that it works the same way as above? Or does it actually stream Internet>Phone>Chromecast (all over WiFi)?