Answer:
The difference between graph will be important, because both of you are setting variables differently, and there can be only one order to this. That is, a graph has two variable, a dependent and an independent one.
In addition, the dependent variable is always represented by the vertical axis, and the independent variable is always represented by the horizontal axis. So, if you graph points (time, distance) that means you are setting time as the independent variable which is correct, because time doesn't depends on any other variable, but distance does depend on time.
Being said that, your friend's graph is wrong because he's graphing points (distance, time), that is, he's setting time as a dependent variable which doesn't make sense.
The main difference between graphs would be that you will have different behaviours, and only one of them is right. Another important difference is that both axis are opposite between your graph and your friend's, because he graphed wrong variables.