Basically, it is degrees of protection. CITES I are the most protected and I believe, CITES I requires permits to sell accross state lines and requires a federal permit to own. CITES I animals (insects and plants as well) are considered very suscepible and are highly regulated. I believe you also need to show cb origin for these to export/import.
CITES II requires CITES import/export papers to ship out of or into the country (but not within a country). CITES III is treated the same as CITES II and differs only in who decides to list the animal as CITES. From the USFW;
"A species is unilaterally listed in Appendix III by a country in the native range of that species, at the request of that country. In contrast, a species is listed in Appendix II by a vote of the Parties."
I believe CITES II and III also need cb certification (which includes farmed animals) to export/import, but there may also be capture/export quotas, I'm not sure on this point.
This is a simplistic explanation and may have minor errors as I am not an expert on this, just somewhat familar with it due to friends who export and geckos I recieve or own.
Regards,
John