For profit schools are in business to do just that, make a profit. Many such schools are owned by corporations. An example is Capella, University of Phoenix, Devry, Ashford University, and Kaplan University.
Non profits exist to not make a profit and normally enjoy tax breaks of nonprofit entities. Most of these schools are your state funded colleges and universities. While the term nonprofit can be misleading, since any educational institution needs funds to survive, this isnt the main goal of these type of colleges.
For profit isnt that bad, there will always be some stigma towards these type of institutions, but with budget cuts happening all the way around, many former nonprofits were purchased by corporations in order to survive. An example is Ashford University and Grand Canyon university, both of these institutions would of certaintly had closed if it wasnt for the fact they were purchased. Now both institutions are fast growing and attracting many students to their programs.