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?
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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.
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.