There may be common sizes but LiPos have various shapes and sizes, many custom for the application. They typically will be rectangular with a sealed polymer bag as the container. Most electronic devices with non replacable batteries or battery modules use these such as laptops, phones, etc. They are efficient in the space used.Ok. I can get behind that. Perhaps flat cell phone style cells or a combo of battery cells to accommodate the case design. All I know is I have two DJI style batteries that are dead after one charge and one flight. No more 3rd party Mavic batteries for me.
Li-Ions on the other hand are cylindrical metal cans with common physical sizes but varying electrical characteristics. You'll likely find these in rechargeable flashlights, cordless phones, etc. Power tools probably use them too.