Open access: The pure form of open access is considered research that's made freely available for reuse in any way another scientist might dream up. In general, as long as the original author is credited for what's his, any other scientist can add to the work with no strings attached.
Public access: By contrast, public access usually describes repositories like PubMed Central, where papers may be made available but can still be subject to various copyright barriers, or may not contain the full article content. Public access can also mean papers are available in locked formats like PDF, preventing them from being mined or analyzed.
Key players: Among open access publishers, some of the largest or best known are BioMed Central (just acquired by Springer), Hindawi, Medknow, and the Public Library of Science. Central organizations in the space include SPARC, an advocacy group for public access, and Creative Commons, which provides access-friendly licensing options for publishers. The Open Access Scholarly Publishing Association is a newly formed group to lobby for full open access.