Projection Specifics in ArcGIS
There are a few different ways we can manipulate coordinate systems in ArcGIS. As was said before, most spatial data we work with has already been assigned the correct coordinate system (the coordinate system that correlates with the values of the coordinates that define the locations of the data). In these cases, we add the data to an ArcMap project and effortlessly the data displays in the correct location and overlays correctly with other data layers in the project whether they share the same data driven coordinate system or not. This is called projecting-on-the-fly. Arc can read the data’s inherent coordinate system and do the correct math behind the scenes to convert the data to any other predefined coordinate system. Projecting on the fly doesn’t alter the data’s origin coordinate system, just does a temporary mathematical adjustment to make it match other data.
Note that the data frame will adopt the coordinate system of the first data layer added to ArcMap will be the coordinate system all subsequent data is displayed in unless the display coordinate system is manually changed.
Reprojecting a dataset means that the user is permanently changing the inherent coordinate system of the data. Reproject is a tool found in the Data Management toolbox and it transforms the root coordinate system of the data to a new one. This is usually advisable for projects with many datasets that are being used in complex analysis. Not necessary to do for simple visualization projection. The tool name is a bit confusing and should probably be changed because it isn’t only used for projected data, but can be used to transform data in geographic coordinate systems (again think curved!) to projected coordinate systems or to transform data in one geographic coordinate system to another geographic coordinate system.
The Define Projection tool again, is ineptly named. It doesn’t just assign projected coordinate systems to a dataset, but geographic coordinate systems as well. This tool is used when a dataset has the wrong coordinate system assigned to it (this does happen often) and a new one needs to completely overwrite the old. This tool is a reboot. It can also be used to define a coordinate system for data that is completely missing one.