I was having the same or similar problem.
I was using a template ‘blog.php’ on a page titled ‘Blog’ to format the posts page.
I was using a template ‘home.php’ on a page titled ‘Home’.
However, every change I made to the ‘Home’ template, also affected the posts page, and ‘blog.php’ template did nothing.
I changed the name of the ‘Home’ template, ‘home.php’ to ‘homepage.php’ and everything is now functioning as I want.
Thanks to everyone above!