I would argue nothing, as neither is properly categorised. Some would say that SEo is organic while search engine marketing is paid. I would say that there is really no such thing as SEO, as we shouldn't optimise for search engines we should market to people. i mostly say internet marketing, website marketing etc. BUT to answer the question, I would suggest the following. SEO - gaining the highest possible position on a search engine for a phrase. SEM - Understanding and researching the area site will operate in, gaining a full understanding of target markets, ensuring that all available keywords and phrases in that niche are being maximised for traffic, and ensuring that the site performs perfectly for search engines and users alike, while also ensuring that there are sufficient quantity and quality of links to the site so that sufficient traffic and link benefit is acquired. By following the above, the site should rank organically in the natural listing, and should be prepared for a PPC campaign. I would also tag on that a good SEM will be able to handle PPC and organic campaigns, and also advise on general opportunities online in your niche.
I would agree with that Temi, I would say though that originally it was called Search Engine Positioning, and there are a LOT of people who are still practicing this.