Below is how my institution differentiates the two:
The word "scholastic" means "of or related to school." So if your school has a Model United Nations Club and your participation in that club explains your award in an "international mun simulation," it would be a scholastic award. If you won an award as editor of your school's magazine, that is a scholastic award. However, if you created a poetry blog or online literary magazine on your own and that effort netted some sort of recognition, it would constitute a nonscholastic award. If you've won local or regional awards through your school's athletics program, those are scholastic awards; if you've won awards by participating in a private sports club, those are nonscholastic awards. The Gold Star Award in Girl Scouts is a nonscholastic award, as is the Eagle Scout Award in Boy Scouts.
MIT didn't used to discriminate between scholastic and nonscholastic awards on the application. Hope this doesn't cause a lot of confusion.
Hmmmm....but since there probably will be confusion, perhaps Mollie could get some definitive statement from admissions to post up in the questions thread above. :-)