Histogram v. Bar Graph: spacing! A bar graph has distinct gaps between variables while a histogram's bars are butted up against each other. The reason for this is show if the x-axis variables are continuous or not. So if you asked what people's choice of drink was in the morning; and your variables were coffee, soda, water, or orange juice, you'd make a bar graph because each variable is unique and independent of each other (Nominal Measurement). However, if you wanted to display how many cups of coffee people had in the morning, you would use a histogram because of 1, 2, 3 cups is a continuous variable (Interval/Ratio Measurement).
A polygon is pretty much a line graph except your line reaches 0 on the x-axis for 1 below your lowest observation and 1 above your highest observation. Honestly I'm not sure of the point of this, maybe it's too show that you don't have data for anything outside those bounds, maybe it's just to make it look like a "full" shape.
