Take Daveed Diggs's who plays Lafayette and Jefferson. Lafayette is the French immigrant whom Hamilton befriends that helps the American army fight off the British. While Diggs's other character is Jefferson, the American ambassador to France who comes in the middle of the play (right after Lafayette leaves, very tricky Mr. Manuel Miranda) and basically tries to destroy Hamilton. Both have ties with the French, but one is Hamilton's friend, the other his enemy.
This is not the only pair of characters like this. You can also look at Jasmine Cephas Jones's characters Peggy Schuyler, the sister that is only in one song and barely mentioned again after, and Miss Maria Reynolds, the women who seduced Hamilton into sleeping with her, and helping her husband make a lot of money in the process. This one is funny because in a sense every Schuyler sister fell for Hamilton throughout the play, Peggy herself may not have, but the woman who looks and sounds identical to her sure did.
The most heart wrenching of the character parallels is John Laurens/Phillip Hamilton played by Anthony Ramos. This one will get you when you realize they were played by the same actor. Both characters wanted to fight for Hamilton so both were involved in duels defending Hamilton, Laurens because Hamilton wasn't allowed to fight, and Philip because he heard someone said something about his father. Laurens luckily making it out alive, Phillip dying while defending his fathers honor. 
Lin Manuel Miranda does an excellent job writing the characters the way he does. It is especially fascinating when you find out about actors playing two roles in paralleling parts.
