Genially curious, which ones? I only know two:
1) khtml based - Chrome/Edge/Safari 2) Gecko based - Firefox
Third would be Servo? Any browser uses it?
(Edge used to use its own engine, EdgeHTML, but switched to Blink and EdgeHTML is no longer developed. EdgeHTML was derived from the Trident/MSHTML engine, which is also no longer developed.)
Blink and WebKit can both trace their history to khtml, but that was a very long time ago.
Chrome used to use WebKit (before Edge existed). Blink was forked from WebKit and they diverged about 10 years ago. They are now considered distinct rendering engines with different behaviours.
So the big three rendering engines today are: Blink, WebKit and Gecko.
All browsers in wide use today use one of those three.
On iOS, all browsers use WebKit due to OS policy restrictions. Chrome and Firefox use WebKit on iOS. This works, and different browsers continue to have their own respective featureson top.
It is widely thought that if Apple loses the power to limit the rendering engine on iOS due to changes in law, so many web devs will drop testing with WebKit browsers that they will pressure users to install Chrome on iOS instead: "Best viewed in Chrome. Some site features may not work using other browsers...". The same way many web devs already dropped testing on Firefox/Gecko. Those site features may become critical, such as abitiy to sign in or view some kinds of data. Apps will ship with parts of Chrome/Blink directly in the app, saving users the decision.
This is what people mean when they say Apple's rendering engine policy on iOS may be all that's preventing most of the web shifting to Chrome/Blink-only dominance, that you won't be able to avoid if you need essential services online.
Excellent description of the situation. I both think people should get to choose their own browser on iOS, and don’t want them to get to choose their own browser for the reason you stated.