The maxim “he who hesitates is lost” means that sometimes if you wait too long to take action, you’ll lose the opportunity to take action altogether. On the other hand, if you’re hesitating before jumping off a cliff, that might not be a bad thing. This proves maxims aren’t always true. By contrast, an “axiom” is something that is accepted as true because it has been proved constantly true in the past, or because it’s so obvious it doesn’t need to be proved again. The word is used most often when speaking of mathematics or logic.
Example: “The science of mathematics is based on axioms that form the foundation for further theories; for example, it is accepted as fact that only one straight line can be drawn between any two points.”