The words are mistakenly used interchangeably by many people, however there is a fundamental difference.
Spiritism is the art practiced by those who work with spirits. Mediums, people who do seances, and those who have (or claim to have) contact with the specific spirits of those who have passed.
Spiritualism is the spiritual path many people these days take in place of an organised religion. Most spiritualists think that what we believe needs to be flexible, ever changing, living, and to do that it can not be contained in books that were written before the invention of the car, before humankind could fly or before we traveled to the moon.