Return current page type

Is there a function that simply returns the current “page type” instead of using is_page(), is_preview(), is_single(), is_archive(), etc?

For example: I can find the current “post type” but I can’t find it’s corresponding “page type”.

You need your own helper function which will return you what you need. It could be like this one:

function wpse8170_loop() {
    global $wp_query;
    $loop = 'notfound';

    if ( $wp_query->is_page ) {
        $loop = is_front_page() ? 'front' : 'page';
    } elseif ( $wp_query->is_home ) {
        $loop = 'home';
    } elseif ( $wp_query->is_single ) {
        $loop = ( $wp_query->is_attachment ) ? 'attachment' : 'single';
    } elseif ( $wp_query->is_category ) {
        $loop = 'category';
    } elseif ( $wp_query->is_tag ) {
        $loop = 'tag';
    } elseif ( $wp_query->is_tax ) {
        $loop = 'tax';
    } elseif ( $wp_query->is_archive ) {
        if ( $wp_query->is_day ) {
            $loop = 'day';
        } elseif ( $wp_query->is_month ) {
            $loop = 'month';
        } elseif ( $wp_query->is_year ) {
            $loop = 'year';
        } elseif ( $wp_query->is_author ) {
            $loop = 'author';
        } else {
            $loop = 'archive';
        }
    } elseif ( $wp_query->is_search ) {
        $loop = 'search';
    } elseif ( $wp_query->is_404 ) {
        $loop = 'notfound';
    }

    return $loop;
}