Saul had dedicated his life to destroying those who had chosen to follow Jesus. Then Jesus offered Saul salvation. Saul accepted the call of The Lord.
Timothy was raised in a household that brought him up to know the Gospel as truth. Jesus invited Timothy to be saved. Timothy accepted. He too became a child of the King.
It doesn’t matter what your background is. Jesus is extending you the opportunity to come to Him for salvation, for a future as his child.