The difference between graphs and charts is mainly in the way the data is compiled and the way it is represented. Graphs are usually focused on raw data and showing the trends and changes in that data over time. Charts are best used when data can be categorized or averaged to create more simplistic and easily consumed figures.
Graphs are meant to be focused on the data in question and how it trends. Graphs have exact numerical figures shown on axes, usually organized on the left and bottom of the graph. Common graph types include dot-and-line and bar graphs. Graphs are most commonly used in analyses and situations that call for raw and exact data.
Charts are designed to show differences in things like surveys and figures in a more aesthetically pleasing way. Charts have numerical figures in line or popping out of the visual representations themselves. Pie charts are the most common type of chart. Charts are used primarily in presentations for businesses and debates.
The difference between charts and graphs are frequently misunderstood because of the similarities in their terms. Graphs and charts both tend to have labels and legends, and the term "graph" is sometimes used in relation to the background of a chart.