Map Projections and Coordinate Systems
Map Projections -- Methods of projecting the spherical Earth on a flat surface
Datum -- Geodetic datums define the size and shape of the earth and the origin and orientation of the coordinate systems used to map the earth.
Coordinate System -- A numeric system for representing locations on a map with a given projection and datum
Map Projections -- Peter H. Dana, The Geographer's Craft Project, Department of Geography, The University of Colorado at Boulder
Coordinate Systems -- Peter H. Dana, The Geographer's Craft Project, Department of Geography, The University of Colorado at Boulder
Datums -- Peter H. Dana, The Geographer's Craft Project, Department of Geography, The University of Colorado at Boulder
This figure shows how using the wrong datum can result in incorrect positioning
In ArcGIS, the map projection, coordinate system and datum are collectively referred to as the spatial reference information or spatial reference system. ArcCatalog can be used to view the spatial reference information of a dataset. ArcCatalog can also be used to create a new version of a dataset in a different spatial information system.
If you add a new dataset to an ArcMap session and it does not have spatial reference information defined you will get a warning message.
ArcMap can project data "on-the-fly" from one projection to another. For example, if you add Dataset A to your ArcMap session that is in UTM NAD 27 then your Data Frame display will be set to UTM NAD 27. If you then add a dataset whose spatial reference information is in something else (e.g. lat/long, state plane) then it will automatically project the data to UTM NAD 27 for display and analysis purposes. It doesn't actually change the dataset, it just changes the way it is natively displayed in ArcMap for that one session.