Chromecast is a feature that many people are now familiar with. It allows the user's phone or tablet screen content to be shared on other screens such as smart televisions or smart monitors. Most manufacturers that support this feature will display the Chromecast built-in label and this will change as Google has rebranded them all to Google Cast.
Google Cast is not a new name. In March 2016, Chromecast was once changed to Google Cast but changed back to Chromecast due to the popularity of Google's affordable dongle at the time. During the announcement of Android Automotive OS a few weeks ago, Google has used the term Google built-in for vehicle manufacturers that integrate Google services on their inforia systems and one of the features is Google Cast.
Even the Android.com website and the Google Support site have also officially used the term Google Cast. In my own review, Google only changed the name of this feature and there were no changes to the features and functionality. For now, the majority of products with the feature of sharing phone/tablet screen content to other screens still use Chromecast built-in. The name change will probably happen in stages.