One template for post attachments and a different one for page attachments?

Create a page_attachment.php and a post_attachment.php file and use this in your theme’s functions.php:

add_filter( 'template_include', 'attachment_template', 99 );
function attachment_template( $template ) {
	if ( is_attachment() ) {
		global $post;
		if ( isset( $post->post_parent ) && $post->post_parent ) {
			$parent = get_post( $id = $post->post_parent );
			if ( $parent->post_type == 'page' ) {
				$template = locate_template( array( 'page_attachment.php' ) );
			} elseif ( $parent->post_type == 'post' ) {
				$template = locate_template( array( 'post_attachment.php' ) );
			}
		}

	}
	return $template;
}

This will make WordPress use the separate files for page and post attachments.

btw:
consider creating a child theme instead of editing your theme directly – if you upgrade the theme all your modifications will be lost.

Thanks keesiemeijer, that’s brilliant and works perfectly! I really appreciate your help.

You’re welcome ??