Admin tabs meta box just like category tabs (Categories/Most Used)

I’m currently building a plugin that adds a meta_box beneath the default Category and Tags meta boxes on edit/add post.

The default Category meta box has two tabs: “Categories” and “Most Used”.

My meta box will have two similar tabs: “Tab 1” and “Tab 2”
See http://i55.tinypic.com/1z6zkft.png

I’ve followed suit with the markup, so my tabs are styled just like the Category meta box tabs. But I could use a hand on how to get them to behave just like the Category tabs.

Does anyone know:

* Do these use jQuery UI tabs?
* How can I reuse/access WP’s javascript to get my tabs to work just like the default Category tabs do?

I’d rather not duplicate functionality or load jquery-ui if the behavior is already available.

Anyone have any ideas here? Can anyone point me in the right direction?

Thanks!