Ever since I updated to 4.0, I’ve noticed that when I tweet or text a link to my website, mobile users are redirected to the email version of my post instead of the post on the site. This is not ideal as tweets don’t render properly, nor do I get the chance to serve popups or in-line subscription boxes.
It does NOT happen when mobile users click the link from Facebok.
What you’re seeing is the AMP version of the post - it’s a version designed for mobile, rather than the email version of your post (although they look kind of similar).
The point of AMP is it loads faster on mobile and gives your site an SEO boost. However, scripts are really restricted, which gives the issues you mention about tweets not rendering and the missing subscription boxes.
Twitter detects the AMP version of your site and uses it automatically. Facebook is not doing that, hence the difference.
AMP is an enabled-by-default integration in Ghost which you can disable: