Google, or should we say Alphabet, has an interesting history with branding. Recently, they changed their Nexus phone line-up brand to Pixel, the parent company renamed itself Alphabet, and now it's Chromecast's turn again.
Earlier this year, the Chromecast ecosystem was renamed to 'Google Cast', but now Google seems to be flip-flopping and wants to go back to the original Chromecast name.
In a confusing turn of events earlier this year, the 'Google Cast' was introduced to consumer devices to "better reflect that Google Cast technology is now supported across a wide range of devices such as Chromecast, TVs, displays, and speakers," as opposed to, presumably, solely streaming web-content.
Now, the new name for third party devices is "Chromecast built-in". The Twitter account is now Chromecast, changed back from Google Cast, and the Google Cast website just threw in the towel and adopted both with the statement "Google Cast - also known as Chromecast built-in..."
— Google Chromecast (@Chromecast) November 22, 2016
The setup app makes matters even worse. The app was 'Chromecast', then changed to 'Google Cast' to coincide with the third-party device launch. Then, it was changed to 'Google Home' to coincide with the Google Home voice appliance announced last month. Whether the app will now revert back to Chromecast remains to be seen.