What differences are shown between Piggy and Jack when Ralph speaks about his father and the queen, in the novel Lord of the Flies?
I might add a little to the answer above (which is a good basis for your answer).
Of course, this episode comes in Chapter Two of the novel, after Ralph has called the first meeting of the boys by blowing the conch. This had led to the appearance of Jack as the leader of the choir, the main group of boys on the island and to their exploration of the island. Jack emerges in this episode as a contender for the leadership of the island, one who, just before Ralph's revelation of his father's naval background, makes claims about what the boys wish for from life on the island. Jack claims that: "We want to have fun. And we want to be rescued.” The order in which Golding has placed these sentences is interesting. Clearly Jack, who was formerly Merridew, the head chorister of a choir school, has previously been the keeper of order. When he first arrives in the novel, he leads a neat line of boys and keeps them in order by bullying them and shaming any who steps out of line. However, as he vies for dominance of the group, he does so by vying to be popular in putting 'fun' before being 'rescued' in order to gain the approval of the younger boys. Conversely, he also acts to promote fear of the 'beast' that one of the other boys claims to have seen in the wood : 'we’ll look for the snake too' he claims. This combination of promoting a popular image of himself and instilling fear in others which he can later manipulate are both key facets of Jack's characterisation at this point in the novel.
Piggy responds to Ralph's words about his father and the hopes of rescue in a considerably more relieved manner. We can see 'Piggy’s open admiration' for Ralph described directly after he speaks the reassuring words about how the navy are bound to rescue them and, indeed, he is contemptuous of the other boys when they rush off with Jack to make the signal fire that Ralph recommends they make in order to help their rescuers to find them:
“Like kids!” he said scornfully. “Acting like a crowd of kids!”
This contempt is, however, partially a mask for his relief. We discover after Ralph's speech that 'Piggy’s breathing was quite restored.' which suggests that his asthma had been brought on by the anxiety of being supplanted by Jack in the hierarchy of the island but that Ralph's seeming control of the situation has left him relieved that he is close to Ralph, the leader, rather than the bullying Jack.
It is telling, however, that even at this stage, the impetuous Jack has already once more taken then lead in his order to “Come on! Follow me!” and that in the rush to do so, the conch, the symbol of democracy and order, lays 'forgotten' as the boys rush to follow Jack who, through force of will, leads the boys away to follow him.
In chapter two of Lord of the Flies, we see that chaos is starting to kick in with the boys. Ralph and Piggy agree that there should be some kind of order, while Jack wants to be wild and free.
"My father's in the Navy. He said there aren't any unknown islands left. He says the Queen has a big room full of maps and all the islands in the world are drawn there. So the Queen's got a picture of this island"
"And sooner or later a ship will put in here. It might even be Daddy's ship. So you see, sooner or later, we shall re rescued".
These two quotes are made by Ralph. He is trying to reassure the boys, that they are going to be rescued and they need to focus on making it easy for ships to spot them. Piggy thinks that everyone is acting like a bunch of children and being disorderly, on the other hand, Jack encourages the boys to start a riot.
Piggy knows that they all need to act with some kind of order and forethought, if they are going to be rescued. Ralph and Piggy want all of them to have to have some kind of rules, but the more the boys are away from civilization the more they are reluctant to follow strict rules. Jack wants to go hunting and be wild and free, and he encourages the other boys to follow him. They want to focus on just having fun, while Ralph and Piggy want to focus on being rescued.