Will tobacco users and nicotine users (like e cigs) test positive for cotinine? Or will they test differently?

Same. They are testing for breakdown products of nicotine so ecigs with nicotine will be detected. .
Testing. Regardless of how one takes in nicotine - it can be picked up with testing for cotinine.
Our Code of Ethics. Do you realize that we really are physicians here? We have a code of ethics under which we operate. Asking us how to beat or cheat on any drug testing process is asking us to break our code of ethics. If you are smoking and you are being tested for it, then lying about smoking (even if it is for cheaper insurance) is fraud and a financial felony. And, of course, continuing to smoke is unhealthy.