Different templates for static pages

I’m using WP for a non-blog website that has three different templates in use on it.

1 for the home page (not an issue)
2 different templates for 2 separate sub-sections, with sub-sections within them.

Those two – I don’t want the funtionality of posts, because that’s not the aim of the site here. I need the funtionality of static pages – however, I don’t know how to call the two separate templates when I’m calling up the posts.

Can anyone help me out with this? I think I may also just be confused… how would you set up such a site?