Hello,
I tested the exercise steps for the “Managing Geospatial Data in ArcGIS” class you mentioned in your post. I was unable to recreate your issue and was able to successfully use the “Feature Class to Feature Class Tool.”
However, the two tools (“Feature Class to Feature Class” and “Feature Class to Geodatabase”) are similar conversion tools but have a few differences to be aware of.
First, the Feature Class to Feature Class tool allows you to “convert a (single) feature class or feature layer to a feature class.” The Feature Class to Geodatabase tool allows you to “convert one or more feature classes or feature layers to a geodatabase feature class.”
Secondly, the Feature Class to Feature Class tool supports field mapping. This allows you to add, delete, rename, and reorder, and change field properties. The Feature Class to Geodatabase tool will simply export the feature classes exactly the way they are.
Finally, the Feature Class to Feature Class tool primarily requires 3 input parameters from the user (i.e., Input Features, Output Location, and Output Name). The Feature Class to Geodatabase tool primarily requires 2 input parameters from the user (i.e., Input Features, Output Geodatabase).
Feature Class to Feature Class Documentation: https://pro.arcgis.com/en/pro-app/2.9/tool-reference/conversion/feature-class-to-feature-class.htm
Feature Class to Feature Class Documentation: https://pro.arcgis.com/en/pro-app/2.9/tool-reference/conversion/feature-class-to-geodatabase.htm