"Khakis" as a term is equivalent to chinos. In terms of english language use, the color name actually follows the article of clothing (actually the cloth), not the other way around. The cloth was tightly woven cotton twill that the British adopted in india- more durable and cooler than the wool they had been wearing. It was typically dyed in tea or mulberry juice, and takes its name from a Persian word for dirt, describing the color.
So yes, this refers to the pants. And the various forms of tan are the most classic, I prefer sand (a much lighter tan) myself, but it's not a contradiction in terms to wear olive khakis, or gray ones. Or navy ones. Black khakis aren't a contradiction in terms, but they are an affront to god.
As for those lists, they're basically to cover what most people in a professional career will need to cover the full range of outfits they might wear in that lifestyle. Edit as you see fit. Khakis are a more casual option, but are perfectly appropriate with a sportcoat in most formal workplaces (though there are still some highly formal environments where they aren't), are usually the default pant option in less formal workplaces, and the standard formal pant option in a casual one (where jeans would dominate). They can also range fairly far into the casual spectrum, making them very versatile. And the fact that they're machine washable makes them easy to take care of, so you can get them dirty and beat them up without too much worry, making them an attractive alternative to wool on a worksite or on a rainy day when you might get various gunk splashed up on your pants.