One important difference is that Airplay is much more of a screen or video mirroring protocol, while Google Cast is focused on the receiver driving presentation, with your mobile device only acting as a navigation source.
Practically, this means that you can take phone calls, hibernate your computer, kill a source app on your phone, leave the house entirely etc. with Chromecast without interrupting whatever's playing on a TV or stereo, while with Airplay, playback usually stops in these scenarios. Airplay is also a bigger battery drain as a result, in my experience.
I had an AirPort Express back in 2004 timeframe that was precursor to Airplay that did beat Chromecast by close to 10 years with AirTunes. AirPlay came out in 2010. Then, in 2017, Apple released AirPlay 2.
Chromecast first gen was in 2013.
Apple actually beat Google on this one in terms of time.
How is a wireless audio technology comparable to chromecast? If it is, bluetooth audio streaming started in 1998, beating airport express by 6 years. And don't get me started on radio...
Practically, this means that you can take phone calls, hibernate your computer, kill a source app on your phone, leave the house entirely etc. with Chromecast without interrupting whatever's playing on a TV or stereo, while with Airplay, playback usually stops in these scenarios. Airplay is also a bigger battery drain as a result, in my experience.