No chromecast is not the same as mirroring. Though you can mirror. Chromecast can send a link to, For example, Play video independent of any device that would otherwise be mirroring it.
I just want my google nest speakers to work with my Roku tv. Was told be someone to buy a google Chromecast hookup for my HDMI plug but then I got to hook up all my tv through Chromecast and that makes Roku useless. I wish they would all work together. Is there an app for that?