permalink and page template path confusion

Hi,

I am creating a site that uses several different child theme template files for each of the menu items e.g. there is a products.php that displays products when the Products menu item is selected. I have defined pages for each of these menu items and associated a template file with each.

So to access a product I enter the url xxx.com/products?prod_id=56

However products are simply posts so the same post could be accessed via the post permalink as xxx.com/post-name-here

So the former uses my products page template file and the latter would presumably use the standard single.php file which I haven’t customised and looks totally different to the products template.

Am I doing something wrong here? Is there a way to simplify things?
Would simply overwriting the contents of a copy of single.php placed in my child theme with the contents of my products.php do the trick?

The permalink structure is currently set as ‘Post name’

Help please anyone.