In the United States, most big national parks are surrounded by national forests. I know that you can do "dispersed camping" in the National Forest, but not the National Park, but other than that, why is there a distinction between the two?
There's a good description of the difference between the two on the National Parks website
The full version is at the link above, but in short :
National parks emphasize strict preservation of pristine areas. They focus on protecting natural and historic resources "unimpaired for future generations." Park rangers work for the National Park Service (NPS) under the Department of Interior.
National forests, on the other hand, emphasize not only resource preservation, but other kinds of use as well. Under this concept of "multiple use," national forests are managed to provide Americans with a wide variety of services and commodities, including lumber, cattle grazing, mineral products and recreation with and without vehicles. The national forests are managed by forest rangers with the US Forest Service (USFS) under the Department of Agriculture.
National Forests are federally owned and protected land, but, unlike parks, they are not neccesarily designated and managed for public use in the same manner as a National Park. In many cases, National Forest land is in fact even leased for commercial purposes, including, for example, many vacation spots and ski resorts.