The answer is an emphatic yes.
National parks emphasize strict preservation of pristine areas.
National forests, on the other hand, emphasize not only resource preservation, but other kinds of use as well. Because they have different purposes, adjoining national parks and national forests may need to have very different rules. For example, national parks usually forbid hunting, while forests usually allow it. Dogs can be taken on national forest trails, but not those in national parks. Both agencies have designated wilderness.