physics are the same regardless the view you use .. so yes, cars should turn the same way .. if not something is terribly wrong .. if you have different feeling it could all be just different FOV for both cameras ... with wide FOV in chase view turns seems to be straighter compared to more realistic narrower FOV ... it can confuse you that you need less steering ..
The difference is all down to perception. Chase view isn't 'connected' to the car like the cockpit view is, the FOV is different, camera angle is different, etc. All of that results in your brain getting different information, which gives you a different feeling.
I have not tested in all sims Pawgy but another is the smaller the FOV can produce more fps, not much but every frame can help
In rF2 sit in pits in cockpit and change FOV real-time with fps counter up you see what I mean
Like the good answers above if you use cockpit and low FOV can make you feel more like you sit in car however it may feel weird till you get used to it, then you never notice it again ...you got to give a few hours etc
By then cockpit will be the only camera feels natural