Just from what I know, top of head without looking it up.

National Parks run by National Park Service. Federally protected lands. There are lot fewer of them. They are more tourist-oriented and are treated like natural wonders for the public to experience. Very high restrictions to protect the land (staying on trail in certain areas, pets, campfires, leave no trace, camp and wilderness permits, manicured roads and trails). Has an entrance fee. Patrolled by park rangers. Often has crowds.

National Forest run by US Forest Service. Also federally protected and managed. There are a lot more of them and aren't marketed with much grandeur as a national park. They often contain a maze of rough, less-maintained forest roads. You can camp anywhere in them for free mostly without any fee or permit requirement, so it's sort of like wilderness. Less stringent rules of what you can and can't do. Very easy to drive into a national forest and see no one around. If I'm ever on the road, I'll sleep in a national forest or other public lands

National Parks, managed by the National Park Service, are designated primarily for preservation and public enjoyment. You're there to observe and enjoy, but not to alter. Activities like logging, mining, and hunting are generally prohibited.

On the other hand, National Forests, managed by the U.S. Forest Service, follow a multiple-use and sustained-yield approach. They're designed to support a variety of activities, including logging, grazing, mining, and recreation. These activities are carried out under sustainable practices to ensure the resources remain for future generations.

https://www.nps.gov/blri/planyourvisit/np-versus-nf.htm#:~:t....

"National parks 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."

Parks are generally more developed with facilities/amenities. NF land is just federally owned forestland. I endorse ngokevin's more detailed sibling comment: https://news.ycombinator.com/item?id=35910185

A forest and a park have completely different uses.

A national park is a place for humans, and to some extent, wildlife, to enjoy,

A forest in this context is a natural resource to be exploited. For the most part it’s a place where lumber is harvested.