Verbal irony occurs when a character says one thing but means another. There is a direct contrast between the character's words and what is intended. A good example would be where a teacher tells a tardy student, "Thanks for being early." Another example is when someone says, "Thanks to the glorious weather, I had to stay at home," when the weather was obviously bad. 

Hyperbole is intentional overstatement or exaggeration. In this instance, what the character states should not be taken literally. The purpose is to make a point or to emphasize. An often quoted example is where an educator tells a student, "I told you a thousand times to do your homework," when the student was admonished only a few times before.

Act 4 of The Crucible provides an excellent example of verbal irony. On a question by Judge Danforth about why he has returned to court, Reverend Hale says the following:  

Why, it is all simple. I come to do the Devil’s work. I come to counsel Christians they should belie themselves. 

Reverend Hale has been frustrated by what he deems the court's indifference to the plight of the accused and its easy acceptance of the girls' obviously concocted testimony. At the end of Act 3, he leaves the court in a huff. He denounces the proceedings and sees it as a sham. Reverend Hale's remark reflects the opposite of his intent. He has now returned to counsel the accused. His purpose is to save their lives, and he begs them to plead guilty to the charges and be rescued from the noose. His motive is, of course, good and in direct contrast to Satan's purpose, which is the promotion of evil.

In Act 1, the Putnams' remarks regarding their children being murdered are hyperbolic. They exaggerate the fact about their children having died soon after being born. They believe that a witch is responsible for their children's deaths. Later in the play, they target Rebecca Nurse as the one accountable. Their nefarious purpose, however, is evident. They are jealous of the Nurses and want their property. Their motives are revenge and greed.

In these two examples, the difference between the verbal irony in Reverend Hale's utterance and the hyperbole stated by the Putnams is evident. The Reverend's remark is a reflection of his exasperation, and his intention is the opposite of what he says. The Putnams, however, intend for their outbursts to be interpreted verbatim. They use exaggeration to emphasize their apparent horror about the tragedy they had to endure. 

It is ironic that Reverend Hale's best efforts to save those doomed to die result in failure, while the Putnams' malevolence triumphs.

Verbal irony is where a person says one thing and means another. Hyperbole is an exaggerated statement which is not meant to be taken literally, but used to prove a point.

Both verbal irony and hyperbole are used in Arthur Miller's play The Crucible.

Verbal irony is seen when Elizabeth is being questioned in court about John's affair with Abigail. Elizabeth is stated to be a woman who will not lie. Unfortunately, to protect John, Elizabeth lies in court and states that he was not a lecher. Readers, Elizabeth and John all know that this is a lie.

A hyperbole is seen when Hale states that if Rebecca is taken to the gallows and hung for witchcraft that all is lost. If Rebecca is hung, nothing will be able to save the rest of Salem. This is an exaggeration given that Rebecca's death does not really mean that all of Salem will die. Hale is simply using this to strike fear into the villagers.

Therefore, the differences between the two is based upon how they are used and the meaning behind their uses. Each is used to try to protect, but they work very differently based upon the defined usage. Readers know that Elizabeth is lying and why she does it. Readers know that the death of Rebecca is an exaggeration based upon the fact that her death does not technically mean all others will die.