This is an important question to consider, especially as some people have always tried (even from the earliest days of the new movement) to legitimise Spiritualism by linking it with Christian Beliefs. In addition there are many books and newspaper articles which try to justify the 1848 events, together with the subsequent contacts with Spirit, by reference to the Biblical Prophecies and Miracles.
However, there is a basic difference to other biblical or prophetic events which is really quite simple to explain. At Hydesville the Discarnate Spirit of an ordinary person communicated with normal people living ordinary lives in the small cottage in a remote hamlet in New York State where the Fox family lived. This was not some prophetic dispensation direct from either God or one of his exalted messengers to a “chosen one,” as some form of new divine revelation.
Indeed New York State had already seen several of these prophetic revelations, to chosen people, in the earlier years of the nineteenth century. The first of these led to the creation of the Mormon Church. The second, predicting an Ascension event where Jesus Christ would come and rescue all of his chosen people before the earth was destroyed, was given to Andrew Miller in 1831. He founded the Millerite Church which spread to both Australia and Europe, carrying the message of Christ’s return sometime between March 21, 1843 and March 21, 1844 to millions of people. After the event failed to occur the church continued but became the Seventh Day Adventists.
However, saying this was a new style of communication is not to deny that there had been previous attempts at such an ordinary communication from the Spirits of ordinary people. Notable examples of this were recorded in the case of the Drummer of Tedworth (a newer work on this can be found here http://eprints.bbk.ac.uk/250/1/Hunter4.pdf and the case of the Epworth Rectory (try the 1917 book The Epworth Phenomena here http://gutenberg.net.au/ebooks03/0301311.txt .
Nor was it to deny that the impact of new religious thinkings, which were based upon claims of such prophetic revelations from God. Most important amongst these was the influence of Emmanuel Swedenborg (http://www.swedenborg.com/ ), whose work was to be a major influence upon Andrew Jackson Davis , the Poughkeepsie Seer, (http://www.andrewjacksondavis.com/ ) who is very important figure in the development of Spiritualism.
Additionally the religious fervour of New York State was another major factor in the rapid development of the movement. I have already mentioned two churches founded there but there were many other sects which spread out from this area. This meant that New York State was an ideal place for Spirit to begin communicating offering a greater chance that this would be more readily accepted. A good history of the district and the events surrounding this period can be found here http://www.crookedlakereview.com/articles/136_150/137fall2005/137martin.html
So Spiritualists treat this new communication in a very different way from past contact with God’s exalted messengers and also differentiate it from biblical miracles. It is seen to be a reflection of natural law, previously unrevealed to us. As the communications have developed our understanding has grown. Additionally through history there have been open minded men of science or psychology who have studied the phenomena of Spiritualism pronouncing them to be real and provable.
The Philosophy and History of Spiritualism 