I noticed however that the definition of medium and medium-well differs significantly depending on the chef. One chef just cooked every order other than well done as medium rare, and no one ever complained.
I subscribe to this, as I've never seen a difference between medium, and medium well. I'm of the opinion that there's "walk a dead cow through a warm room", "rare", medium rare", "medium", "well done", and "toast". I've also never understood the need of some people to deride anyone for going to well done, it's their meet, and if they like it like that then so be it.
As a note, many places (particularly franchises, or chains) in the U.S. will not cook a steak less than medium anymore. This is because of the recommended internal temp of 141 (about 60 Celsius). There are plenty of exceptions, but if you eat out a lot, and you like rare steak, you'll notice this.