From all the reading I've done, it seems that the definitions of these stamps are somewhat debatable. I've come up with the following categories:
1. Illegal Issues: bogus stamps from real (or imaginary) countries that are meant to appeal to collectors but that were not issued by the postal authorities of the countries in question and have no postal value. The Universal Postal Union puts out regular circulars listing bogus issues and it has a searchable database of member postal services and their issues, which are cataloged according to the WDAP Numbering System (WNS).
2. Local Issues: stamps issued by a locality that have no postal value, distinguished from illegals in that they do have local postal value. There is probably some overlap here. Staffa, Scotland, for example, seems to be an uninhabited island, but, according to one site I found, has been issuing "local" stamps for the better part of forty years. This site lists some genuine local posts as well as some bogus ones, and more information can be found though the Local Post Collectors Society.
3. Poster Stamps (which were used for advertising), Labels (e.g. matchbox labels). and Seals (generally for a charitable organization like the WWF).