What is the difference between a marriage cancellation and a divorce?

Rightly or wrongly I am going to assume that by "marriage cancellation" you mean "annulment". Divorce occurs when either or both parties go before a court of law and become legally separated. Some churches or religious bodies recognize the divorce and as far as I know, allow the parties to marry again. The Roman Catholic Church does not recognize divorce. However, they will allow an annulment if it can be proven that the marriage was not a marriage to begin with. For example, the Roman Church believes, as many other Faiths do, that amongst other things, marriage is for the purpose of procreation. If it can be proven that either party did not marry for this reason they may refer the matter to the Church for annulment.

These annulment cases are referred to The Roman Rota in The Vatican for debate. The Rota is a body of high clergymen skilled in Canon Law (Church Law). This can be a very lengthy process, sometimes taking many years to resolve. If both parties are prepared to wait for this process to take it's course, they may receive an annulment and are free to marry again. The Roman Church take their stance on divorce from The Bible - I cannot quote chapter and verse, but I will paraphrase what I remember from my readings of the Bible: "What God has joined, let not man put asunder". I have answered this question to the best of my ability. If anyone can improve on it, please do so!