gui design - n-to-n selector UI

I am looking for a name of one specific UI element. I have unsuccessful tried to identify it before but this attempt failed.

What I am looking for is an n-to-n selector where items move between two states. Lets say you have two buckets (states), one on the left, one on the right. There are multiple items in the left bucket and you can move them to the right bucket and back.

What is the name of this element? How is it different from normal list where you can select multiple items?

Answer

The UI element you are referring to is called the List Builder

Reference: http://msdn.microsoft.com/en-us/library/windows/desktop/dn742407.aspx#usage

List builders allow users to create a list of choices by adding one item at a time, and optionally setting the list order.

A list builder consists of two single-selection lists: the list on the left is a fixed set of options and the list on the right is the list being built. There are two command buttons between the lists:

1. An Add button that moves the currently selected option to the list being built, inserted before the selected item. (Double-clicking on an option item has the same effect.)


2. A Remove button that removes the selected item from the built list and returns it to the option list. (Double-clicking on an item in the built list has the same effect.) The built list may optionally have Move Up and Move Down commands to order the list items.