Shapefiles and file geodatabase (.gdb) are two distinct formats for geospatial data storage.
Shapefiles are standalone entities, while file geodatabase is only the container in which
tables (aka "feature classes") live.
The meaning of "change the coordinate system" can differ greatly -- what, exactly, do
you need to do? [From what, to what?]
Odds are, you'll need to process each table sequentially, probably into a new FGDB.
- V