Search Engine Compatibility
Search engine compatibility is making your site easy for search engines to crawl through and parse. Think of a search engine crawler as an honored guest to your site. You don't want to piss it off by being a bad host with issues like broken links, slow page load times, site outages, broken HTML, flash-based navigation, text in images, unstable urls, a poorly configured robots.txt… Googlebot is a busy little guy with a big web to crawl. Make his life easier.
I also put title tags and meta description in this category of search engine compatibility because when the search engine tries to display your page in its results, it wants to show a title and description. If those don't exist, then the search engine just has to make it up.
There are great tools like Google Web Master Tools, BrightEdge, and SiteBeam to help you with search engine compatibility. Use them!
If you want a page to rank highly on a search result, you need to use language that people are likely to search for. Theresa Regli (@TheresaRegli) has a great story from her taxonomy work at Yankee Candle. Apparently, internally Yankee Candle calls those jar candles "Housewarmers;" but the rest of the world calls them "jar candles." Nobody but an employee (or the most loyal customer) would search for a "housewarmer." It looks like Yankee followed Theresa's advice and both terms are used on the site. I think that it is a good idea to have both because some people will see a candle (which is labeled housewarmer) and type housewarmer into a search to buy one. If you are Yankee Candle, you want your housewarmer/jar candle category landing page to be the top result.
All this keyword standardization sounds obvious. Of course you want to communicate with words that your audience thinks in. It is a little less obvious when you are dealing with a global site because you need to know what terms people in different markets are going to search for.
Search Engine Exploitation
Search Engine Exploitation encompasses the dark art of trying to understand how the search algorithms work and then gaming them to your advantage. We don't do this and don't recommend that you do it either. Any advantage you gain will be short-lived and possibly followed by penalties. It is much better to develop good content that a reader would like and work with the search engines to connect their users with it. That makes it a win-win. You should stay away from SEO experts that brag about their intimate knowledge of how the algorithms work and their ability to trick them.
More precise language is always better when communicating. Hopefully, these terms will help you have more productive conversations about increasing traffic from search engines. Start with search engine compatibility and look for the worst offenses. If your site goes down all of the time, fix that as soon as possible. Outages hurt more than SEO. Then verify that the robots can walk through your site. I have had a couple of clients with a robots.txt that denied all access to the site. In both cases, those directives were put in place before the site was launched and never removed. Good navigation also critical. Every page you want indexed needs to be navigable (linked to from somewhere). Once you have made your site accessible to the crawler, then focus on keyword standardization to tune how you communicate with how your audience thinks. This may change over time as you adjust your strategy and also as language evolves so you need to keep on top of that.