The USDA regulates the possession, importation, exportation, and interstate transport of arthropods under the Plant Protection Act of 2000. Unfortunately, due to the diversity of regulated arthropods, the regulations are somewhat vague, and species-specific information, especially for species that are kept as pets, is hard to find on the USDA site. The USDA recently published a list of species that were deregulated, but other than some large cockroaches, this list does not help most hobbyists much. I have spent many hours on the phone with USDA entomologists and will do my best to fully clarify the restrictions on pet arthropod ownership in the US. Keep in mind, though, that I do not make the regulations, and state laws can restrict arthropods that are not regulated by the USDA. Also, unidentified species from a taxa listed as unregulated may be regulated as this list is designed for well-known, common species.
To explain the permit types, there are different movements mentioned. An importation permit and an interstate movement permit are separate, and importation permits often stipulate stricter requirements for maintenance of the organisms on the permits. Nevertheless, both should be obtainable for a private hobbyist, and one can hold both an interstate movement permit and an importation permit for the same species.