What is the mean of "On Page SEO"? Is it related to mark-up , accessibility and semantics?
Edit:
Does "On Page SEO" requires input from XHTML Coder? Is it a job of developer?
incrediman answered almost all parts of your question. Here are some of my thoughts which I believe is helpful to you.
As you saied, usually we tend to split SEO into two parts, On site and off site.
First let talk a little bit about off site SEO. Since Google and other search engines put special weight on links, both internal and external, people usual try to build in-bound links from other relevant sites. This is basically called OFF SITE SEO.
Then On-site SEO. It is arguably the most important part of SEO, and we can boil it down to two parts too, one is content related, another is code related.
Code related on site SEO refers to write semantic code, build user-friendly web site structure, remov dead links , design sound internal links(contrary to off-site SEO) and so on.
Regarding to content related SEO, it usually marketers' job to take care of. There is a saying that content is the king, and that means good title, mata description, keywords and so forth are extremely important to consider when you do SEO.
Plus, IMHO, On-site SEO and On-Page SEO are basically the same except on-site SEO inclines to build whole site structure, especially internal links between different pages on the site.