what is the difference between using the tool "DEFINE PROJECT" to define a coordinate system to my shape file or Feature Class, and use from since right click --> Arc Catalog and choose one simply from the file specified .It reaches the same?
In both cases you define or assign (or replace) a coordinate system to a featureclass. The result is the same.
The tool however, allows for usage in ModelBuilder and in python scripts (and other coding languages). This way you can automatically apply a coordinate system to multiple featureclasses, while with the manual method (ArcCatalog) you will have to repeat the same process for each featureclass.
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