Yes, sometimes you can use different graphs interchangeably, perhaps to demonstrate a different property of the statistics you are using. But you have to ask yourself: what am I trying to demonstrate? How many variables are you measuring? Are you working on a correlation between two variables and do you want to see if there's a correlation or connection between the two? Or is there only one variable?
In one case you may decide to use a line graph to look at possible correlation, so using a pie chart or circular graph would not be a good idea as an interchange. But a pie chart and a bar graph could be used interchangeably. If you were going to present statistics to an audience you would want to use appropriate charts to give the best impression of your statistics. A line graph is good for showing trends, for example (crime figures, wages, average global temperature, etc.)