There are some pretty big differences between the characters and events, although the basic premise is the same. Here are some differences:
1. Abby was only 11, and John Proctor was in his 60's. Elizabeth wasn't his first wife, and his kids were grown. He owned a "pub," or a local pool-hall. Abby and John did not have an affair.
2. The girls were not dancing in the woods. They were actually cracking eggs and dropping them into glasses of water; whatever shape the egg took in the glass was supposed to indicate the profession of their future spouse. So, for example, if the egg shaped like an anchor, their husband would be a sailor; if it shaped like a plow, they would be a farmer. This was considered fortune-telling, and strictly forbidden in their community. One girl's egg turned into a "coffin," and all of the girls freaked out and thought it was some sort of punishment for what they were doing. That is how the original hysteria began. Other sources contribute their hysteria to illness caused by mold found in foods and breads; this has less historical support though.
3. The trials actually faded and stopped because so many people were confessing to witchcraft to save their lives, not the other way around, as the movie version indicates.
4. The Putnams had not lost all of their children.
5. Giles Corey actually was pressed to death, but not for refusing to give the name of the witness against Putnam. Instead, he was accused of witchcraft, and he refused to enter a plea of guilty or not guilty. If he were to enter a plea, that put the case into the courts, which meant that his lands would have been forfeited to the state, and he wanted his kids to be able to have his land for an inheritance. So, he did not enter a plea so that the land would remain his. That is why he was killed.
Those are just a few key differences; there are many more. However, Miller did stay true to the premise behind the trials, which is that mass hysteria and lack of logic led to the deaths of many innocent people. The concept of having fears and accusing others for petty reasons does hold true. Also, 19 people actually did hang, and Corey was pressed to death, so that stays true to events. I hope that those thoughts helped; good luck!