Site Title and Tag Line(Both are) Show on my Meta Title/ Site Title

You can use the wp_title filter to change your title to whatever you want.

add_filter( 'wp_title', 'my_title', 10, 2 );
function my_title( $title, $sep ) {
    global $page, $paged;
    if ( is_feed() )
        return $title;
    // Add the site title to the page's title
    $title .= get_bloginfo( 'name' );
    // Add the tagline to homepage (remove the 3 below lines if you don't need)
    $site_description = get_bloginfo( 'description', 'display' );
    if ( $site_description && ( is_home() || is_front_page() ) )
        $title .= " $sep $site_description";
    // Add a page number if necessary:
    if ( $paged >= 2 || $page >= 2 )
        $title .= " $sep " . sprintf( __( 'Page %s', 'text-domain' ), max( $paged, $page ) );
    return $title;
}

The above code will update your blog’s title depending on where you are at the moment.

Please notice, your theme has to support the title tag. If it does not, you should add the support by using add_theme_support( 'title-tag' ); in your theme’s functions.php file.

Feel free to change the above code and add / remove the parts you would like to see or hide.