MMUI: the Miva Merchant User Interface, also know as the Miva Merchant Look and Feel. This is a standard "Look and Feel" module that comes with every store. Some modules may require code changes to work with MMUI. If listed as MMUI compatible and code changes are required, installation instructions will be included with the module. Payment, shipping, export, import, utility and logging modules generally require no changes to the MMUI.
OpenUI:the Open User Interface, also know as OUI and Open Look and Feel. This is a module that replaces the MMUI while keeping the same look. Essentially, it allows third party developers to "hook" modules into Miva Merchant. We don't sell the OpenUI directly however we do carry a guide to Miva Merchant that includes a free copy of the OpenUI. As it happens, this combination works out considerably cheaper than buying the OpenUI directly elsewhere. You also do not need to wait for the book to be delivered--we can email you a copy of the OpenUI and the license key soon after your purchase. The book is listed here.