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MDX is an extension to the SQL language which Microsoft utilizes to query and script access to multidimensional data. You can use MDX queries to get at data stored in a SQL Server Analysis Server cube by bringing back facts based on dimensions with hierarchies.
UDM, on the other hand, is the name that Microsoft gives to the data structures used to store data in Analysis Service. For example, when you create a start schema in SSAS with dimensions, facts and hierarchies, you have created a unified dimensional model or UDM. This is how the data is stored in the cube, while MDX is the language you use to query the data stored in the cube.
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