Yes, I can see now that you are right. My apologies. I have now searched some of the 'history.' I have to admit that after installing 'Chrome' to my Lumia phone I had not got round to looking at it properly. Now I have.
I was expecting a slimed down version of the Chrome Portable I have on my Tablet's SD memory card (D), downloaded from Portable Apps.com or PortableApps Freeware (I dont remember which) --- as far as I know it is 'genuine' and has the Chromecast app which is what I mainly wanted. What was (I have now uninstalled it) on my phone seems nothing more than a searching app, although it has lots of links to Google products / webpages, which gave me the wrong initial impression.
I do know there are a number of ersatz versions of Chrome around.
As for wanting Chrome on my phone I now know I dont need the Google Chromecast app to Cast from my phone, only an app which integrates with Chromecast and I have found a couple of those (for YouTube and local media, for example).