I'm fairly new to editing software and I intially downloaded Lightroom (desktop and mobile), but I'm reading the book by Tony Northrup which he is talking about lightroom classic. Do they have the same capabilities, same thing just different name, or is one better than the other?
There are major differences. Lightroom stores your photos in "the cloud" and allows sharing from "the cloud" to any device. Lightroom Classic stores your photos on your computer or attached hard drive or attached network drive; offers less flexible cloud sharing. There are also feature differences.