10001: Layer's data source has a different projection <value> than the data frame's projection
A layer in your document is in a different coordinate system than your output display (that is, the coordinate system of the data frame). This requires on-the-fly projection, which can affect drawing performance. The <value> parameter of this warning message indicates the projection of the data source.
Solution
Check the drawing performance for your layer or basemap layer in ArcMap. If you are publishing, check the drawing performance for your service in the Preview window.
Learn more about working with basemap layers or previewing your service
Pilot test your map document to see if map performance is too slow. In some situations, on-the-fly map projection for some datasets may not degrade performance too severely. For example, datasets with a small number of simple features (such as points or line and polygon features with very few vertices) may display relatively quickly in spite of the need to perform on-the-fly projection. If you see a need to make changes, reproject your dataset into a common coordinate system that is the same as that of your data frame.
More information
The data frame's coordinate system need not be the same as the data you are using. However, if the data frame has to project your map layers on the fly, it takes longer to draw.
Each data frame in ArcMap has a coordinate system used for its output map display. This can be any coordinate system that is supported by ArcGIS. It is typically based on the map layers in the data frame because, by default, the data frame's map projection is initialized to the map projection of the first map layer that you add in ArcMap.
How to determine the coordinate system for your data frame. Right-click the data frame for which you want to determine the coordinate system and click Properties to open the Data Frame Properties dialog box. Then, click the Coordinate System tab. The details of the current data frame coordinate system are shown on the dialog box.
Changing the data frame's coordinate system. On the Data Frame Properties dialog box, you can change the data frame's coordinate system.
How to identify the coordinate system of a map layer. Each map layer has a data source (such as a feature class, raster dataset, and so on). You can right-click a layer in the ArcMap table of contents and click Properties. Next, click the Source tab and scroll through the information on the Data Source panel. The coordinate system details are shown on this panel.
Changing the coordinate system of a map layer. You must reproject the original data source used for the map layer. See the Project geoprocessing tool for more information.