I think it would be best to start with some definitions so that we have a base level to begin with. So, I have gone to Wikipedia and grabbed their definitions:

• Search Engine Optimization (SEO) is the process of improving the volume and quality of traffic to a web site from search engines via “natural” (“organic” or “algorithmic”) search results
• Search Engine Marketing (SEM) is a form of Internet Marketing that seeks to promote web sites by increasing their visibility in the Search Engine results pages (SERPs) and has a proven Return on Investment (ROI).
• Pay Per Click (PPC), or Paid Placement, is an advertising model used on web sites, advertising networks, and search engines where advertisers only pay when a user actually clicks on an ad to visit the advertiser’s web site.
• Paid Inclusion is a search engine marketing product where the search engine company charges fees related to inclusion of web sites in their search index.
• Key Performance Indicators (KPI) are financial and non-financial metrics used to quantify objectives to reflect strategic performance of an organization.
• Web Analytics is the study of the behavior of web site visitors.

My personal perspective expands the definition of Web Analytics to include the measurement of SEM, including paid inclusion, pay-per-click, organic search results, and SEO.

Here is how I see the relationship between all these:

What do you think? Are there better ways to diagram or describe the relationship? Do you agree or disagree with these definitions? Leave your thoughts here in your comments.