.........................
I applied the contrast before, by increasing the 'contrast' as it's called in Premiere Pro. Now the contrast is not applied at all in the second video.
It has been said before: don't use the contrast effect in Premiere. I provides little control and you don't know what you are doing while moving the slider.
I repeat: NEVER use the contrast effect. I tis close to useless.
Better use color wheels, levels or curves to control contrast.
The s curve is still adding saturation on it's own though.
Because you influence the contrast in the image, you influence the saturation.
REMEMBER THIS: contrast is NOT the name of an effect. Contrast is a concept to discus the amount of 'opposite values' in an image/sound/story/whatever: small vs big, black vs white, treble vs bass, loud vs silent, empthe vs. crouded, and so on. (Affinity is the opposite of contrast.)
Applying an s curve pulls shadows down and raises highlights while the lowest and highest values can stay the same (unless you move those end points).
If the camera is already applying enough of an s curve, is an s curve in post necessary then?
If the image from the camera is they way you want it, you indeed don't have to do anything with it.
That is what I was referring to: you need to look at the image, understand scopes and waveforms, calibrate your monitor with a real tool, and understand the tools to manipulate the image to be able to change it in a way you actually get what you want.
Just applying a S curve because you read that that is the way to go, you are making up dogmatic rules again. Rules you aren't supposed to make anymore, right?
Never* do something, because it is a rule, but because it helps to get the image you want.
(* This applies to filmmaking only. Don't break rules in traffic, unless following the rules will kill/hurt you or someone else. Don't break the law or you'll be in trouble. The same goes with breaking promises to your spouse

)
So: you your eyes and brain.
If I should remove the s curve in the camera, how does one do that with an Canon DSLR?
Have you ever tried to take a picture with a Canon?
Did you ever shoot a picture in the RAW format?
Did you ever open a RAW picture (you know .cr2-file) in Photoshop?
Did you ever see the menu on the right for the curves?
Did you ever look at it?
Did you ever notice that in raw file the standard setting is a 'normal contrast' and that you can also choose 'lineair contrast' (or something like that) and 'high contrast'?
Choose the lineair one. This shows the RAW photograph without S curve applied to it.
(I would appreciate it if you quoted this list and replied to every question. Otherwise nobody but you (??) will understand whether you understand what I say here.)
One does not remove s curve in a Canon, one can only lower contrast. Which is the closest you can get.
Recap in short:
s curve is not the holy grail to get a great looking image.
It is just something that is used for footage shot in a certain way to get a certain look or basic look to work from.