A graph is a representation of a topic and shows the values usually in lines or bars. Mostly, a graph represents something that we count. We could count the numbers of blue and red cars in a street and show our findings in a graph.
Or the hectares of the rainforest.
Or the rainy days in a week.
Or our income or pocket money and the way we spend it.
Therefore a graph shows a relationship between characteristics (2 or more), with the means of a line, curve, bars or other symbols. Typically there is a horizontal line (x-axis) to represent an independent variable and a vertical line (y-axis) to represent a depending variable.
Chart is another word for graph.
BASIC CHARTS are bar charts, line charts, pie charts.
MORE ADVANCED CHARTS can be used to show more complex matters.
There are many different kinds of graphs.
In general the graphs differentiate in usage.
Which form of graph you use depends on what you want to say or show.