Jimmy and Bob were friends in their youth because they grew up together in the same neighborhood in New York. But they had different characters even then, and their characters led them down different paths in life. Bob was materialistic. He wanted success and didn't care how he obtained it. His ambition led him into a life of crime. Jimmy, on the other hand, valued honest, hard work, and respectability. He stayed in New York and became a policeman. Bob fails to recognize him because it never would have occurred to him that Jimmy might become a policeman.
Bob's nickname of "Silky" suggests not only that he is a smooth character but that he likes luxuries such as silk--silk ties, silk scarves, silk shirts, silk underwear, etc. After twenty years he has achieved material success, but he is obviously all alone in the world and a stranger in his own hometown of New York.
O. Henry doesn't tell us much about Jimmy, but he is probably married, has children, and goes to church every Sunday. Having remained in New York all these years, he probably has lots of friends. He obviously enjoy security as a policeman and should have a comfortable retirement.
Bob reveals the difference in the two friends' characters even when he was only eighteen and Jimmy only twenty.
"You bet! I hope Jimmy has done half as well. He was a kind of plodder, though, good fellow as he was. I've had to compete with some of the sharpest wits going to get my pile. A man gets in a groove in New York. It takes the West to put a razor-edge on him."
O. Henry is not merely being ironic in this story. He is expressing his own philosophy that a simple, honest, and secure life is preferable than a dishonest life that may bring prosperity but also brings rootlessness, loneliness and insecurity. The theme of "After Twenty Years" might be expressed very simply in the old folk saying, "Honesty is the best policy."