What is the difference between MiraCast, MirrorShare, Google Cast and Chromecast?
Google Cast and Miracast are 2 different technologies and protocols.

Miracast primarily allows wireless screen mirroring, and support is usually built-in in the OS in modern Android devices and Windows 8.1+.

Google Cast additionally allows transferring external multimedia stream to the remote screen without decoding it on the mobile device, but support for this depends on the application.

Miracast is often branded with proprietary label, most probably, in your case MirrorShare is Miracast.

Chromecast may refer to either the Google Cast protocol or a dongle which allows to use Google Cast on the TV without built-in support.