Earth-613 follows the exact history of Earth-616 up until the assassination of Steven Rogers.
In this reality, Steve Rogers actually was shot to death. The Avengers managed to capture the shooter, and they scrambled for a replacement for Steve. After testing Clint Barton with the shield, he accepted the mantle and became the new Captain America. This caused a mental breakdown in Hank Pym, who had been growing more fragile. He began mass-creating Ultron robots and used them to siege New York City, killing several Avengers and imprisoning anyone who dared defy him. Along the way, he accepted a select group who would help him along the way. The remaining heroes scrambled to form a resistance to fight the reign of Pym.
Captain America would later be taken during Cap-Verse.