If you want to display comments and the comment form on posts but not on pages, you need to split up the logic in your template file to call comments_template() depending on the type of the item displayed (post or page). There are two ways to do this: either you keep one template file for both items, and use conditional tags:
if (!is_page()) {
comments_template();
}
The other option is to use both a single.php template file for your posts and a page.php for your pages (see the Template Hierarchy for more information). Just leave out the call to comments_template() in the page template. If there are no other differences between a post and a page layout, one combined template file with conditional tags is probably better for maintainability.
If you want to do this “from a distance”, so where the template file already includes a call to comments_template(), you can create a plugin that hooks into the comments_template filter and redirects it to an empty file in the directory (well, it could even be the plugin file itself – since it only contains PHP code, it won’t display anything – but this will be confusing to others).
add_filter('comments_template', 'no_comments_on_page');
function no_comments_on_page( $file )
{
if ( is_page() ) {
$file = dirname( __FILE__ ) . '/empty-file.php';
}
return $file;
}