What is the difference between a discrete uniform distribution and a continuous uniform distribution?
One way of knowing discrete or continuous is that in the case of discrete a point will have mass, and in continuous a point has no mass.
this is better understood when observing the graphs.
Let us look at the Discrete first.
Take a look at its pmf
notice how the mass is sitting on the points?
now look at its cdf
notice how the values go up in steps, and that the line is not continuous? this also shows how there is mass at the point on the pmf
Now we will look at the Continuous case
observe its pdf
notice how mass is not sitting at a point, but between two points?
and now to look at the cdf
here you can see on the cdf that the function is continuous, is does not go in steps that that on the discrete case.
I had pulled these images of wikipedia, so here is the reference to the pages, where you could also read up a bit more on the topics.