Other than models and a single-shot rifle Browning did not make any guns. He licensed his designs- sometimes he sold them outright- to Colt, Winchester, Remington and Fabrique Nationale (Belgium). His orginal contract with FN was in 1898 for a .32 ACP pistol that became the FN Model 1902.
I dont think FN ever made a .45, but don't know for sure. If they did it was only experiemental.