Hardly a day goes by that I do not see these two words used interchangeably. However, they have very different meanings.
DISINTERESTED means unbiased. It does not mean you do not care; you might care very deeply about an issue but are sufficiently open-minded that you will consider other points of view.
UNINTERESTED means you do not care, that you have no interest in a particular situation.
If you were accused of a crime, would you want the judge and jury determining your fate to be disinterested or uninterested? It could make a big difference.