Honestly I've often wondered this question and even though I had a little bit of an idea, I wasn't quite sure I was right. So I did some research. For the most part, people use the terms contests and sweepstakes interchangeably. Every now and then you will get an avid person that is adament that they be called what they are. Sometimes you can see these complaints in the comments section of our contests/sweepstakes.
If you want to get serious about it, the term contests means that in order to win, you have to have a bit of skill. For instance, you have to be the best photographer, write a recipe, answer questions, have the best caption, video, etc. These contests are free to enter, but you have to do a bit of work in order to be the winner.
On the flip side of contests, sweepstakes are really a game of chance. There is no skill required unless you count entering on a continual basis. Generally sweepstakes carry bigger prizes than contests so you just might get that new car or a cash prize that you have been dreaming of if you focus yourself in this area. I suppose that's why some members are serious when they discuss sweepstakes and contests. They want them to be called exactly what they are so there is no confusion. I have even read in our message board that some members only enter sweepstakes and never enter contests. Personally I look at the prize, not what is in the title of the contests/sweepstakes. If it's something I want to win, I enter it even if it does fit in the lowly category of contests.