There is no clear-cut line of demarcation between a diagram and a graph yet -
A graph needs a graph paper but a diagram can be drawn on a plain paper. In the technical way we can say that a graph is a mathematical relation between two variables. This however is not the case of a diagram.
As diagrams are attractive to look at, they are used for publicity and propaganda. Graphs on the other hand are more useful to statisticians and research workers for the purpose of further analysis.
For representing frequency distribution,
diagrams are rarely used when compared with graphs. For example,
for the time series graphs are more appropriate than diagrams.