The most important difference between these two kinds of entities is that non-profit organizations, of course, are not trying to make any profit. They, therefore, do not have the same goal that corporations have.
However, this is not the only difference. Another important difference is in the sorts of goods and services that they produce. Non-profits are generally trying to produce some sort of public good such as clean air or better schools. This is different from the consumer or capital goods that are usually produced by for-profit organizations. Another difference is in the type of labor that the entities use. Non-profits rely to a large degree on donated volunteer labor.
There are a number of other differences as well, but these are the major ones. Please follow the link to see more.