Hi,
The map units are determined by the spatial reference of the map. The map control does not support client-side reprojection on the fly in the same way the ArcGIS Engine MapControl does - so typically you do not explicitly set the spatial reference of the map but it is determined by the first layer you add. This is usually your "basemap" which will typically be a cached/tiled service (ArcGISTiledMapServiceLayer) or local tile cache (LocalTileCacheLayer in Beta 1). Other layers/services which are then added to the map need to match that projection. ArcGIS Server dynamic services and local ArcGIS Runtime dynamic services will support reprojection on demand.
The World Street Map service (http://services.arcgisonline.com/ArcGIS/rest/services/World_Street_Map/MapServer) is in the Web Mercator Auxiliary Sphere projection (3857/102100) and the units for this projection are meters.
Cheers
Mike