site:example.com returns content that's not mine

[Broadway]

I just did a google search for my site's pages in the google index:
site:example.com
(My preferred form is www.example.com. I've declared that in WMT and do non-www to www redirecting in .htaccess)

With the site:example.com search -
My site's home page is returned as the first item in the SERPs, shown as www.example.com.

The URL's of the next 8 SERP items shown on the page take the form:
https://example.com/articles
https://example.com/blog/
https://example.com/terms/
https://example.com/events/

All of the rest of the SERP results (on page 2 and beyond) seem to be my regular URLs with the www.example.com form.

First off, my website doesn't use https.
Second problem, the titles and descriptions shown aren't content from my website.
When I click any one of the links, I get the notice "This connection is untrusted." (I assume this is my browser that shows this warning?) Because of that I've not gone to the actual page (don't know if there could be something there harmful to my machine).

The titles and descriptions shown on the offending links appears to be content from a very legitimate website.
And, in fact, when I search for the keywords in the titles and descriptions I find the same pages, but under the URL of that legitimate site (first registered in 2001, expires in 2018).
I've looked at that site. It seems real, just a regular corporation.

I don't understand what is going on here or what to do to resolve this matter. Help please.

[aakk9999]

When I click any one of the links, I get the notice "This connection is untrusted." (I assume this is my browser that shows this warning?) Because of that I've not gone to the actual page (don't know if there could be something there harmful to my machine).

Yes, this is your browser displaying the message. This is the standard message when a site that does not have https is tried to be accessed via https protocol.

You may want to talk about this to your hosting provider - there may be some sort of misconfiguration there.

I have encountered a similar problem in the past when the hoster has pointed a domain to a wrong webspace.

[Broadway]

ok thank you. That's what I needed, a place to start looking.
I did initially check to see if the other website involved used the same hosting service.
I didn't get the impression they did, but anyway I'll start there.

[Broadway]

Thanks again aakk9999.
My account had recently be switched to a new server.
On that server, the "default" https setting redirected incorrect https requests to that second website (a configuration error), and that's what Google then picked up as the URL and content (for the non-existent URL request).