How do you determine if a result in a search query is a post or a page?

That will only tell you if it’s a Post or a Page. What if it’s a category, tag, archive, or custom post type? Here’s how I’d write that, if you care.

function xyz_get_post_type_name() {
    $wp_type = get_post_type( get_the_ID()  );
    switch ($wp_type) {
        case 'post' :
            $type_name="Article";
        break;
        case 'page' :
            $type_name="Web Page";
        break;
        case 'quote' :
            $type_name="Testimonial";
        break;
        case 'post_tag' :
            $type_name="Topic";
        break;
        default : 
            $type_name = ucfirst($wp_type);
        break;
    } // END switch
    return $type_name;
} // END xyz_get_post_type_name()

Then just echo that function inside your loop wherever you want it.

while ( $searchQuery->have_posts() ) : $searchQuery->the_post();
    echo 'Post Type Name: ' . xyz_get_post_type_name();
endwhile;

The switch statement would also allow you to give these post types a “pretty” name and default to just their actual name (first letter capitalized).