We use these words (ok, maybe not chinois so much) interchangeably to describe something, usually metal, that holds solid ingredients while liquid passes through it. It's a strainer, a colander, a mesh thingy, whatever. In reality, there are differences, especially when it comes to that chinois... A strainer is really a catchall name for any type of, well, strainer. It is usually fine mesh and bowl-shaped, good for rinsing a pint of berries or draining pasta.
A colander is typically a larger bowl-shaped strainer, often with bigger holes (although that's not always the case). We think of colorful plastic or metal strainers that sit on their own base rather than need to be held by a handle. Our thoughts are this: The little mesh thing we use to catch seeds while we squeeze lemons? Strainer. The footed bowl that holds up to a big dumping of pasta or five pounds of nectarines? Colander.
And then there's the chinois. These can get expensive, and the best ones come with a wooden pestle for mashing ingredients against the sides. They are cone-shaped, which allows for more straining surface area, and they are used mostly for making sauces, soups, and custards that need to be super smooth and silky. The holes are extremely fine, and you can use the pestle to pulverize every last drop of liquid out of the solid ingredients without mashing through any grit.
We read an article from Chow describing the difference between a colander and a chinois, with suggestions for good ones. The author also mentions something called a Superbag, which allows you to squeeze ingredients in a flexible mesh bag to eek out the liquid. Might be a nice investment for someone who needs a chinois but lacks space to store it.
Read the article here:
*Update: My mom just emailed to tell me that, growing up in Mississippi, she called a chinois a "foley mill." Does that ring a bell for anyone else?
A little more about the chinois and why it differs from a china cap: Word of Mouth: Chinois