Trying to find a way to use Python or SQL to loop through geodatabases and print the feature classes. I'm not sure what the difference between while and for loops are; I'm brand new to scripting. A point in the right direction would be great.

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If you're asking about Esri geodatabases, arcpy.ListFeatureClasses does exactly this given an input workspace (e.g. geodatabase connection).

The code (Python 3) from their example:

import arcpy
import os

arcpy.env.workspace = "c:/base/gdb.gdb"

datasets = arcpy.ListDatasets(feature_type='feature')
datasets = [''] + datasets if datasets is not None else []

for ds in datasets:
    for fc in arcpy.ListFeatureClasses(feature_dataset=ds):
        path = os.path.join(arcpy.env.workspace, ds, fc)

A while loop is used because we don't know how many items there are so the loop continues until it reaches the last item. A for loop is used when you want to explicitly determine how many times the loop will be executed.

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