Comparison of geodata formats
ESRI proprietary formats
ESRI ArcInfo Coverage - Ancient, dead format still widely in use by people clinging to the last remaining copies of ArcInfo. ESRI no longer provides any reasonable documentation. Good luck. I don't have to tell you not to use these because either you won't listen to me because you can't move on or you have never heard of them. See this Library of Congress doc: https://www.loc.gov/preservation/digital/formats/fdd/fdd000284.shtml
Personal Geodatabase - deprecated, based on obsolete 32-bit Microsoft technology. Don't use these. Organized as SQL data inside a "JET" (aka "Access") file with an ".mdb" extension.
File Geodatabase - aka FGDB - File based, still highly proprietary but accessible via an API that is free. Organized as a zillion files inside a directory with a .gdb extension. Don't look inside the folder! It's just data in there.
Layer file - When you save a layer file, the file filename.lyr is created for the layer to store symbology design and layout information, so that you can reuse those settings in other maps.
Open formats
Shapefile - Pretty much "owned" by ESRI but everyone has adopted it. A "shapefile" is really a collection of files with the same name but different extensions.
The projection (if it is defined) is stored in filename.prj. This is an ASCII file. You can cheat and copy and rename it to define projection on other shapefiles; of course, this does not reproject data. Shapefiles created with ArcView 3.x do not have prj files.
Tabular data for attributes is stored in a DB IV format file called filename.dbf
When ArcCatalog creates metadata for the file, it puts it in filename.xml.
Data interchange formats
ESRI ASCII (e00) format