As far as I know they do not work together or interact.
What I know is both can receive music from a mobile device using an app that includes the cast icon. I have a few apps like this and have cast music from a source (e.g. my PC's Chrome browser, or my iPhone, iPad or my home network) to either (but not both simultaneously) On Home, music plays and I can ask Home what is playing and get a reply. On the Chromecast/TV the visual shows album art, title and artist. Since my TV audio is input to the stereo system, sound is great.