Therefore, a photographer, regardless of the amount or types of equipment he carries, is not subjected to any particular restriction other than those which apply to the general public. If you need to go to an area closed to the public, or be there at a time when an area is closed, of course you need a permit, but so would you even if you were not photographing. Generally speaking with editorial and fine-art work, there is no need for a permit, because you'd be photographing only what is found in the park, and not using a crew. Even if your photos are going to be used as commercial stock, as long as they are taken in accordance with the quoted paragraph you don't need to apply for a special permit. You also do not need any type of property release, as long as you're not photographing a private property inside the park.
Releases protect a person's right of privacy.
Public lands have no such right. On the other hand, some types of commercial photography requires a permit. This is loosely defined by the NPS as anything which requires you to have a model, crew or props, and includes wedding photography. The rules were mostly intended towards motion picture production and commercial product photography, which can cause a significant disruption to sites. If you want to run a workshop in a NP, you need a Incidental Business Permit, since this is considered commercial usage.