I always find this such an interesting feature of our federal government.
Inside the national parks, the agency is the National Park Service, which is part of the Department of the Interior. Outside the national parks, the agency is the Forest Service, which is part of the Department of Agriculture. Then also there is the Bureau of Land Management stuck into a few areas. Each agency does things their own way, they have their own rules, and they get different partner companies to do their housekeeping.
The only good thing is that if you start within a park and your backpacking trip extends out of the park, or vice-versa, you can normally do it all on one wilderness permit, which is from where you started.