Arrgh! My head is swimming with buzz-words! I am wading through this material as best I can, but I could sure use a Rosetta stone to help steer me through the terminology and concepts. I have come to suspect that any time someone can't recall the term that applies, they simply make up a new one on the spot.
On-page SEO refers to things you do on the page itself to make sure it is spider friendly and to clarify the page's topic in ways that the search engines will understand and respond well to.
Off-page SEO refers to things you do elsewhere on your site(s) or on the internet at large to improve how the search engines perceive your page. The biggest focus there is link development, which can be achieved and fine-tuned in a variety of ways.