So the dobro played horizontally by Jerry Douglas is one kind of lap steel on its own
It is, and you break these things down a million ways but for ease of reference in musician terms you would usually just say lap steel (electric), dobro (acoustic).
In dobro for example you could have a steel guitar like a National, or a wooden guitar, a square neck like Richard has, or a round neck. Where does it end?
The main thing is a lap steel (electric) like on Daddy's Gone to Knoxville, sounds very different to a dobro like on All That Matters and that's why it's useful to make a distinction. In my opinion anyway.