I don’t consider these similar. Presumptuous is a negative adjective. It means you assume (“presume”) something inappropriately. If you are being presumptuous, you are assuming, for example, that I will do something for you. The word implies that this assumption is not correct, that we don’t know each other well enough for you to assume that I will do the thing you want me to do. Therefore you are arrogant, or self-centered, to think that. Example: Could you drive me to the airport? Well that’s presumptuous, we’ve only known each other for two days and it’s a five hour drive. Example: I am at a hotel, and I demand the best suite, although it is already reserved. That is presumptuous (I am assuming (presume) that I am more important than the person that has reserved the room. Audacious is a generally positive adjective. I means to be bold, to be brave. It is a strong adjective, not used frequently while speaking. In the United States being audacious is considered good - to be so bold that it is out of the common way, that you draw attention to yourself. Example: My friend hiked 3000 kilometers solo (solo means by herself). It took the entire summer. That was audacious!