I am a little confused about how variables are related to distributions as one moves from descriptive statistics to inferential statistics. I know that a variable in descriptive statistics is some measurable characteristic of some phenomenon, and its distribution is some description (table or graph) of how the values of this variable vary. This seems fairly comprehensible. But then I was introduced to the concept of a random variable, and its associated probability distribution. My main question, what is the difference between descriptive statistical variables and random variables, and what is the difference between a the distribution of a regular variable and a probability distribution of a random variable? They seem like analogues, but I am just not seeing the "big picture" in terms of what I am doing in statistics with these random variables, distributions, and probability distributions. If anybody could give me a clear description of how I should be thinking about all of this, it would be greatly appreciated.