I see no difference whatsoever between digital and analog photography. Saying digital isn't actually photography is like saying that Da Vinci's work isn't real because it wasn't painted on the inside of a cave, using the rear end of a squirrel dipped in mud and lizard poo.
A camera is a tool, like a chisel or a CNC router.
Regarding what I see when I take a photo sure, the digital camera isn't an exact representation of what I actually see, what my eyes convey through my visual verv to the brain but neither is film. I don't see in black and white and the colors I actually see don't look anything like the colors captured on Portra 400 or any other color film that I know of. The beauty of it all is that I'm free to choose whatever tool, digital or film, that will allow me to approximate what I visualize in my mind andc I an guarantee you that what goes on in my mind has very little to do with reality.
Now I have to go find my jar of lizard poo...