There are quite a few differences between the appearance of the ghosts in Hamlet and in Macbeth, differences in how the ghosts affect the plot, what they do, and the effect that they have on the protagonist of each play.
First, the ghost of Hamlet's father provides major plot information, crucial to setting up Hamlet's main objective in the play -- to revenge his father's murder. This ghost relays the details of his murder, which prompts Hamlet towards revenge.
On the other hand, the plot of Macbeth does not hinge upon the actions of the ghost of Banquo. The appearance of Banquo's ghost does signal a turning point for Macbeth, but Macbeth's move away from guilt and concern over the human lives he is destroying to fulfill his objective -- to acquire and maintain the Kingship -- is the result of many events, of which the appearance of Banquo's ghost is only one. So, the appearance of Banquo's ghost is not crucial to setting the plot in motion, in the way that the ghost of Hamlet's father is.
The ghosts also behave differently. The ghost of Hamlet's father appears to many people. In fact, the play is set up so that the audience and other characters see the ghost and confirm its presence before Hamlet ever does. This ghost has a mission, and he fulfills it in relaying his story to Hamlet. The ghost of Hamlet's father also reappears in Act III when he suspects that Hamlet is not fulfilling his assignment. Again, this ghost has a mission to fulfill in the plot of the play, and it drives his behaviour.
The ghost of Banquo's behaviour is much more mysterious. Does he wish Macbeth ill? Does he want to forgive Macbeth? To frighten him? All of the questions are valid, since the Ghost does not explain its presence. It also remains unclear whether this ghost even actually appears as anything other than a figment of Macbeth's imagination. No one else sees this ghost, and it does not speak. And, in this case, Shakespeare has already cast doubt upon Macbeth's clarity of vision, because in Act II, Macbeth imagines that he sees "a dagger." Could Banquo's ghost be another such imaginary vision? Most definitely. So, Banquo's ghost's behaviour and reality remains a vision surrounded by unanswered question.
Both protagonists are struck with a bit of wonder at the sighting of the ghosts, but while Macbeth seems terrified and wishes the ghost of Banquo gone, Hamlet resists the restraint of those around him and follows the ghost eagerly and without fear. He wants to hear what the ghost will tell him, as it confirms his suspicions about his uncle. Macbeth wants no part of the ghost of Banquo, as this ghost's appearance only magnifies and confirms his guilt as Banquo's murderer.
Overall, the ghosts in the plays Hamlet and Macbeth serve very different purposes and have completely different effects upon the protagonists and audiences of each play.
First of all, I would like to appreciate the above expert who has nicely explained. According to me 'ghost' used in a play suggests the thoughts of a mind. In the play 'Hamlet' ghost was the answer to the questions always haunted Hamlet. Probably he kept on thinking why he did not have his father, how he died etc. Shakespeare took advantage of such thoughts to put in the plot and the ghost plays a vital role to take the plot to its climax.
On the otherhand, the ghost of Banquo saw by Macbeth was his reactions for guilt. Banquo was his friend and he murdered him only to make his throne gree from any successor. Predictions of the witches in the second meeting are also the outcome of his own mind. He thought himself that none could vanquish him. It was ipossible like a wood walk on its feet or any man born of woman could defeat him. Thus after having murdered Banquo, he feared of this foul deed and so he saw Banquo everywhere during feast. It took the plot to the climax by the suspicion raised in the minds of others and then making them confirmed. They took it for granted that Banquo was murdered by Macbeth himself.