Graphs vs Diagrams
Sometimes, the information purported to be understood is too long and complex. To make it interesting and understandable in an exciting manner, different visual representations are used. Graphs and diagrams are two of the common means to visually represent information that is either repetitive in nature or too complex. There are similarities in these techniques that confuse many to treat them as similar. However, there are differences that will be highlighted in this article.
Diagrams
We are too well aware of the use of diagrams to explain information and facts that are presented in the form of text. If you need to explain the parts of a machine or the principle of its working, it becomes difficult to make one understand the concept through text only. This is where diagrams in the form of sketches come into play. Similarly, diagrams are made heavy use of in biology where students have to learn about different body parts and their functions. Visual representation of concepts through diagrams has better chances of retention in the memory of students than presenting them in the form of text.
Diagrams are resorted to right from the time a kid enters a school as even alphabets are presented to him in a more interesting and attractive manner with the help of diagrams.
Graphs
Whenever there are two variables in a set of information, it is better to present the information using graphs as it makes it easier to understand the data. For example, if one is trying to show how the prices of commodities have increased with respect to time, a simple line graph would be a more effective and interesting way rather than putting all this information in the form of text which is hard to remember whereas even a layman can see how prices have gone up or down in relation to time.
Graphs make use of graph paper which has precise squares and presents the information in an accurate manner and the reader can see the effect of one variable on another in a very simple manner.
Difference Between Graphs and Diagrams • All graphs are a diagram but not all diagrams are graph. This means that diagram is only a subset of graph. • Graph is a representation of information using lines on two or three axes such as x, y, and z, whereas diagram is a simple pictorial representation of what a thing looks like or how it works. • Graphs are representations to a scale whereas diagrams need not be to a scale • Diagrams are more attractive to look at which is why they are used in publicity whereas graphs are for the use of statisticians and researchers. • Values of mean and median can be calculated through graphs which is not possible with diagrams • Graphs are drawn on graph paper whereas diagrams do not need a graph paper • For frequency distribution, only graphs are used and it cannot be represented through diagrams

Jon Bresler says
You have your concept of subset backwards