You both have the right idea, but you'll actually need both fitlers, one to catch the button text, another to catch the localised text, so a combination of the two.

This works..

class MyClass {
    function __construct() {
        add_action('admin_head-post.php',     array ( $this, 'load_gettext_filters' ), 1 );
        add_action('admin_head-post-new.php', array ( $this, 'load_gettext_filters' ), 1 );
    }

    function load_gettext_filters() {
        global $post_type, $wp_scripts;
        
        if( 'YOURTYPENAMEHERE' != $post_type )
            return;
        
        $wp_scripts->registered['post']->extra['l10n'][1]['publish'] = __('Save');
        
        add_filter( 'gettext', array ( $this, 'change_publishing_text' ), 10, 2 );
    }

    function change_publishing_text( $translation, $text ) {
        if( 'Publish' != $text )
            return $translation;
            
        return __( 'Save' );
    }
}
$MyClass = new MyClass;

You both have the right idea, but you'll actually need both filters, one to catch the button text, another to catch the localized text, so a combination of the two.

This works..

class MyClass {
    function __construct() {
        add_action('admin_head-post.php',     array ( $this, 'load_gettext_filters' ), 1 );
        add_action('admin_head-post-new.php', array ( $this, 'load_gettext_filters' ), 1 );
    }

    function load_gettext_filters() {
        global $post_type, $wp_scripts;
        
        if( 'YOURTYPENAMEHERE' != $post_type )
            return;
        
        $wp_scripts->registered['post']->extra['l10n'][1]['publish'] = __('Save');
        
        add_filter( 'gettext', array ( $this, 'change_publishing_text' ), 10, 2 );
    }

    function change_publishing_text( $translation, $text ) {
        if( 'Publish' != $text )
            return $translation;
            
        return __( 'Save' );
    }
}
$MyClass = new MyClass;