mysterious redirects

I wish I knew how to label this problem. If I knew what to call it, I probably could find someone else had already answered the problem.

I have several pages we’ll call:

https://mysite.com/directory/page-1
https://mysite.com/directory/page-2
https://mysite.com/directory/page-3

If I browse to those pages using a navbar or URL I am redirected to similar but different content.

https://mysite.com/2010/10/10/stuff-about-page-1
https://mysite.com/another-directory/page-2/
https://mysite.com/related-directory/page-3-stuff/

I first noticed this a couple of days ago and started by disabling and then deleting the Smart 404 plugin. I restarted Apache. I can’t figure out what’s causing these links to redirect. I liked it back when I could actually look at an .htaccess file (but that was long ago).

Here’s what’s bizarre. If I go to the WordPress Dashboard and then edit one of the pages and then click on “View Page” I’ll see the correct content. 2 seconds later if I browse to the content any other way I get the redirected content.

Help!