TITLE: Probability density function vs. probability mass function
QUESTION [93 upvotes]: I've a confession to make. I've been using PDF's and PMF's without actually knowing what they are. My understanding is that density equals area under the curve, but if I look at it that way, then it doesn't make sense to refer to the "mass" of a random variable in discrete distributions. How can I interpret this? Why do we call use "mass" and "density" to describe these functions rather than something else?
P.S. Please feel free to change the question itself in a more understandable way if you feel this is a logically wrong question.

REPLY [5 votes]: The most basic difference between probability mass function and probability density function is that probability mass function concentrates on a certain point for example, if we have to find a probability of getting a number 2. Then our whole concentration is on 2. Hence we use pmf however in pdf our concentration our on the interval it is lying. For e.g.$ -\infty <= X <= \infty $. 
Always remember that discrete and continuous are dependent on the Range.