Multiple thumbnails and one gallery

It is possible but it needs some developing effort. First of all it is important to know that WordPress default »galleries« are not discrete resources you can address with an separate URL. They are just shortcodes defined on a single posts context.

So what you need to do is to define a URL the thumbnails point to which, of cause, defers from the posts thumbnail. One (not the only) way is, to add a rewrite endpoint to your permalink. Assuming your post permalink is your-domain.tld/2014/a-wordpress-post/ the URL the thumbnails could look like your-domain.tld/2014/a-wordpress-post/thumb/123/. The number on the last part represents the ID of each thumbnail. Endpoints are normally added on init:

add_action( 'init', 'wpse_131753_add_thumb_endpoint' );
function wpse_131753_add_thumb_endpoint() {

    add_rewrite_endpoint( 'thumb', EP_PERMALINK | EP_PAGES );
}

Now, you need to change the way, WordPress renders the gallery shortcode. There’s a filter for that called post_gallery. It bypasses the output of the default function called gallery_shortcode() which is defined in wp-includes/media.php.

Let’s view some code for this:

add_filter( 'post_gallery', 'wpse_131753_gallery_view', 10, 2 );
function wpse_131753_gallery_view( $output, $shortcode_attributes ) {

    $default_attributes = array(
        'show-thumbnails' => '',
        'order'           => 'ASC',
        'orderby'         => 'menu_order ID',
        'id'              => $post ? $post->ID : 0,
        'itemtag'         => 'dl',
        'icontag'         => 'dt',
        'captiontag'      => 'dd',
        'columns'         => 3,
        'size'            => 'thumbnail',
        'include'         => '',
        'exclude'         => '',
        'link'            => ''
    );
    $atts = shortcode_atts( $default_attributes, $shortcode_attributes, 'gallery' );
    $current_thumb_ID = get_query_var( 'thumb' );
    // build your gallery markup here using
    // $atts[ 'show-thumbnails' ] and 
    // $current_thumb_ID
    // to defer between varous outputs

    if ( $current_thumb_ID ) {
        // here you may want to show the compltete gallery
    } else {
        // and here you may want to show the thumbs in 
        // $atts[ 'show-thumbnails' ]

        // to link to the detailed view use this:
        $permalink = untrailingslashit( get_permalink( get_the_ID() ) ); 
        $thumb_link = $permalink . '/thumb/' . $thumb_ID; 
        // where $thumb_ID is one of the IDs in your atts.
    }
    return $output;
}

The function sould lookup for the default used gallery shortcode attributes and build the html on your belief whether it should show only the three thumbnails when no endpoint is given or a specific thumbnail was clicked (the endpoint contains the ID of the clicked thumbnail). The enpoint’s value is stored in the query variable: get_query_var( 'thumb' ).