Well, characteristic functions are more general than MGFs (in that they are always finite) and have very useful properties, but they have a similar definition a

Well, characteristic functions are more general than MGFs (in that they are always finite) and have very useful properties, but they have a similar definition and are also based on an expectation. This may be pedantic, but an object that determines a distribution that isn't based on expected values is the CDF. In my first probability course in undergrad I think we defined probability mass functions and probability density functions first and defined CDFs in terms of them, but from a measure theoretic point of view, the CDF is more fundamental since it is defined for continuous and discrete distributions (and also for distributions that are neither).