There is always that discussion about whether Superman or Clark is the real personality
This has been covered in comics then on screen
Taking it that Kal El never got to grow up on Krypton under Jor El
Like how Tarzan was not the Lord Greystoke he would have been if he grew up in England
The Dean Cain version works on "Clark is who I am Superman is what I can do "
The Chris films are taken as the description given in Kill Bill
Superman was born Superman
Clark is the disguise
And it has been noted about how Clark was rejected by Lana while Superman is accepted by Lois
It is Clarks human emotion that comes out here
Jor El tells Superman he is not to interfere with human history
Jonathan over rides this
You are here for a reason
So at this point Clark not Kal El truly becomes Superman, no restriction, pushes his power to the limit and literally turns back time