Commonly known as a "Bamix" I think because these guys invented them, all the commercial chefs I've worked with call them Stab Mixers.
Let me know if you've heard another term, but when I say "Stab Mixer" in Australia everyone knows what I'm talking about.
Oil and water don't mix by themselves, they're like, well, oil and water. Try it, put half a cup of oil and half a cup or water into a blender and start it off. You can wait a week and it will still just be a spinning oil slick.
The only way you can get these two old enemies to co-operate is with an emulsifier.
On the molecular level an emulsifier has a water connector and an oil connector, so mixed in with them it will stick to both and they will all combine.
Classical Cookery revolves around a bunch of basic sauces, Mayonnaise, Hollandaise, Jus etc, and then things are added to them to make other sauces, but they aren't really whole new recipes by themselves, so they are called derivatives. This makes life easier for the working cook, as he or she only needs to remember the foundation recipes and the derivatives of them. If you were in a commercial kitchen listening to chefs talking to each other you would hear them saying things like "Make a basic brown sauce and add mushrooms and thyme to it" - the assumption is that everyone knows what's in a basic brown sauce, but the house sauce has these extra ingredients in them.