Ultimately, the Putmans believe in witchcraft and Rebecca Nurse does not. However, when really looking at the motives behind the accusations, it becomes a little bit more complicated than that.
In Act 1, when we are first introduced to "sick" Betty, the Putnams come in and immediately try to convince Reverend Parris that withcraft is involved. While it seems that they believe in witches, Miller also explains to readers a bit of history behind the Putnams. Mr. Putnam has some grudges against many people because of property disputes and other things. He feels that he has been wronged in his life, so it is likely that he is only using accusations of witchcraft as an opportunity to get back at people who have wronged him. It is up to the reader to decide whether he truly believes in witchcraft or not. Quite possibly, he has convinced himself that witchcraft is real because of how strongly he wants to get back at people.
Mrs. Putnam's motivations are a bit different. She jumps to witchcraft because she has had many children die at birth, and she wants someone to blame. It might seem more believable that she blames something supernatural for the death of her children. Of course she, like Putnam, is still siezing an opportunity to blame someone else for her troubles.
Rebecca Nurse is much more sensible than the Putnams. Upon seeing Betty and hearing the initial whisperings of witchcraft, says
I think she'll wake in time. Pray calm yourselves. I have eleven children, and I am twenty-six times a grandma and I have seen them all through their silly seasons, and when it come on them they will run the Devil bowlegged keeping upwith their mischief. I think she’ll wake when she tires of it. A child’s spirit is like a child,you can never catch it by running after it; you must stand still, and, for love, it willsoon itself come back
Rebecca Nurse is wise in her years, and practical. She sees the girls' behaviors for what they are- silly antics- and knows that people should not overreact. Unfortunately, it is the Putnams' attitude toward witchcraft that wins out in the end. People feed into the hysteria, and those like Rebecca Nurse who try to make people see the truth end up paying with their lives.