If you want to use Chromecast when watching via a web browser, you will need either a computer with Google Chrome or an Android device with Google Chrome, and the Chromecast icon should appear as expected. iOS devices with Google Chrome can unfortunately not be Chromecast at this time.
If you want to use AirPlay via a browser, an iOS device in combination with Safari is required for it to work.
Platforms that have apps through us have full support for both AirPlay and Chromecast. If you experience problems via AirPlay, try sending the signal via AirPlay's built-in function if you are using screen sharing.