Page.php or page-template.php never used. Index.php always used

I have a custom theme.
In the theme, there is a page.php file and a page-template.php file

When creating a page, the template drop down list shows both templates

default template
another template

No matter which template I choose, index.php is always used. I’m not sure what I did to cause this catastrophe to occur. It does not happen on twentyfifteen. This occurs whether plugins are activated or not.