How do I render a navigation menu like my theme does?

I am using the theme suffusion, and I’m trying to add a custom navigation menu to only one of my pages.
I’ve managed to get it almost working using this in my page template:

if(is_page('123')
{
    wp_nav_menu( array( 'menu' => 'my-menu' ) );
}

Where '123' is the page id of the page that I want, and 'my-menu' is the menu I want. The page is using the correct template. The correct items are generated with appropriate links, but they are rendered as an unordered list like so:

• Item 1
• Item 2
• Item 3
• Item 4

If I have the menu bar rendered by my theme (by placing it in one of the slots in the dashboard), it renders this menu horizontally as attractive-looking buttons.

When I do it this way, it correctly only shows up on the page that I want, but is rendered as a vertical bulletted list.

What do I need to change so that the menu is rendered as if done by the theme?