I think we're all confused and, in the end, I think it's all Google's fault. Here's what happened. I went to my old Google home-page a day or two ago (it comes up automatically as my default when I click on Internet Explorer). Everything was fine except that on my gmail page I could view the page but couldn't open any mail. An orange banner told me I had better switch to Google Chrome. So I clicked on that. I got all that google-plus crap along with the Chrome download. Never specifically asked for it at all.
As I said in my OP, I now have two Google avatars sitting on my screen and use the Chrome one only if I want to read my mail. The old one works just fine for accessing A2k or FaceBook or anything else I want to look up.
But, as I said, I'm confused.