Kill Bill has the classic explanation, that Superman is who he is and Clark is the disguise, making him the opposite of the other heroes mentioned, Batman and Spiderman 

Lois and Clark 

This version has Kal El accepting that Clark is the real identity, the person he has been his whole life, while Superman is just the costume he puts on to allow him to use his powers in the open - 

"Superman" was never meant to develop as a separate personality, that happened after Clark in disguise as "Superman" had to interact with people 

The Blur in Smallville just turned up, took action, and raced off - nobody saw anything more than the blur, so he never had to interact and develop an identity, as "Superman" or anything else