When WordPress Default table, Echo Success. When Plugin Table, Echo Blank

$wpdb does not contain any reference to custom tables. So the uap_banners property doesn’t exist. You need to write in the table name the say way it was written when creating the table. So in your case that would probably be (assuming you included the database prefix):

$user_checks = $wpdb->get_results( 
    "
    SELECT id, name
    FROM {$wpdb->prefix}uap_banners
    "
);