What I have been told the differences were
The 4000 was a lighter version of the 4020. I have heard it referred to as the “4020 with the 4010 rear end”. The only real differences that I know of were the castings in the rear were lighter, no differential lock, and I read fewer synchronizers. The rest of the tractor was suppose to be the same, the motor, cooling, Hp,etc. I don’t know the differences on the power shift version. I have spent many hours on a 4000 and and many more on several 4020’s. As far as the lights, scv’s and the pre-cleaner (air-stack) I’ve seen 4000’s with the same set-up as the 4020 and vise versa. I think these were all options. The 4000 I ran had 2 SCV remotes , 2 lights per fender, no pre-cleaner, and was not a “dash“ model. I have a very good friend that has a 4020 with one light per fender, and is a dash model (1968).
I have a Deere book that said the reason for it was to do the same amount of work as a 4020, but with smaller implements. To pull a 4 btm plow fast enough to cover the same ground as the 4020 with a 5.