Do Catholics refer to all martyrs as Saints? At first I was thinking the only requirement to be canonized was to be killed for your faith. Is this accurate? How is someone deemed a Saint as opposed to a martyr in Catholicism?
The process is called canonization.  Wikipedia's article on canonization describes the process.  Martyrdom is not a requirement for sainthood, although being martyred does suggest that a person may very well be a saint (think John 15:13, Greater love than this no man hath, that a man lay down his life for his friends.).  Mother Theresa is a great example of a non-martyred saint, canonized because of the great witness of her life of love and compassion for the poor in India.

In summary, a person is recognized by a bishop or other church person with sufficient authority as a possible candidate for sainthood, and an investigation is started.  The Congregation for the Causes of the Saints investigates this information, and eventually may make a recommendation that the pope make a declaration that the Servant of God is 'heroic in virtue'.  At this point, the potential saint becomes known as 'Venerable', meaning that Catholic may encourage veneration of this person, such as prayers for intercession, but the church has made no official statement on whether or not it is believed that the person is in Heaven.  

The next step is where martyrdom matters.  If the Pope makes a declaration of martyrdom, then the martyr can be canonized, as the Catholic church teaches that all martyrs go to Heaven, and being in Heaven is the definition of a 'capital-S' Saint.  

If the person was not a martyr, then the person is considered a 'confessor', a person who bore witness to Christ (confessed Christ) through the way they lived their life.  A miracle achieved through the intercession of the venerable must be documented before a confessor can be beatified, and can be called "Blessed" (but still not a saint yet!).  There are strict guidelines in evaluating miracles to determine their authenticity.  For a confessor to be canonized, and declared a saint, two miracles are required.

Note that this is a summary, and I am leaving details out - such as requirements for time to pass before canonization.  Also, I am not an expert in Catholic canon law; while the general information is accurate, I could have details wrong.  If you want to hear from an expert, you could go to Catholic Forum's Ask an Apologist subforum and send in your question.