A graph, a chart, and a plot can all refer to the same thing. Is there any even somewhat consistent distinction in these three words?
(I mean, in this particular sense of the words; it is not relevant that a chart is also a nautical map, a plot is also a scheme, and a graph is also an unrelated mathematical object.)
The terms partly overlap, at least if they are used somewhat loosely, and in that overlap there isn't really any difference.
A graph is a diagram of a mathematical function, but can also be used (loosely) about a diagram of statistical data.
A chart is a graphic representation of data, where a line chart is one form.
A plot is the result of plotting statistics as a diagram in different ways, where some of the ways are similar to some chart types.
So, a line chart could be called a graph or a plot, while a pie chart is neither a graph nor a plot. A scatterplot is a chart but not (strictly) a graph, but the purpose of a scatterplot is to determine if there is some relation that can be expressed as a function that then naturally can be drawn as a graph.
Chart and graph are essentially synonymous, but there are some cases where one is preferred over another. This Google Ngram "chart" shows their relative uses:
From this we can see that "bar chart" and "bar graph" are used about as much as each other (and have been since the early twentieth century). "Line graph" is strongly preferred over "line chart", and "pie chart" is strongly preferred over "pie graph" (though in my own AusEng I think "pie graph" feels more natural.)
Plots are different. We make plots out of points, and for something to be a plot, both axes must be continuous. For example, you can make a plot of the height vs. weight of a population, but not the height vs. species, because species are discrete; you can't plot a point halfway between a cow and a chicken. So I'd say that plots are a subset of charts/graphs.
(source: ablongman.com)
In my professional and academic writing experience, I have never encountered a style guide that defines rules for these words.
I am Australian, an engineer (former) and a mathematics teacher and I consider the following to be best practice when writing and teaching.
Therefore…
I “teach” this but wouldn’t enforce it.
The etymology of the suffix -graph supports my practice. Scratching with a stick produces a line. But could also produce a pictograph, figure, diagram etc.
The etymology of both chart might support my practice, in that it is derived from words meaning “map”. A map is a pictorial or symbolic representation.
The etymology of plot might support my practice. Areas of land are typically divided into square or rectangular “plots”. Rectangular areas correlate with the notion of coordinates (sides of a rectangle). Furthermore, variations of plot in other languages typically mean marking points on a chart.
Other supportive uses…
The word photograph seems to deviate, unless you imagine that it’s a new way to “draw” with light, the old way being with a pencil on paper.
Here's a quote from a book called "Basic Allied Health Statistics and Analysis"
A chart illustrates data using only one quantitative coordinate. Charts are most appropriate for quantitatively comparing discrete categories or groups of data. The most common charts are column, bar, line and pie charts. [...] A bar chart is particularly useful for displaying data such as gender, ethnicity, occupation, types of discharges, and treatment categories. Bar charts are appropriate for displaying categorical data. Bar charts compare categories or groups using some quantitative measurement.
A graph is a method of relating one qualitative [I think this a mistake, and it's meant to say 'quantitative'...] variable to another quantitative variable, usually time. The most common graphs are histograms and frequency polygons. [...] Quantitative continuous data are displayed via a graph. The two most commonly employed graphs are the histogram and the frequency polygon.
So it seems charts are for when there's one qualitative variable (such as type, preference, or gender) and one quantitative variable (such as time, age or amount). These include pie charts and bar charts. Whereas graphs are for when you have two quantitative variables.
Chart and graph are not synonymous.
Consider an Eye testing Chart for example - there is no graph on that.
Consider a Pie Chart - there is no graph on that either.
Consider a Look-Up Chart - there is no graph on that.
Consider a Heat Map - that is also a type of Chart.
A graph can be ON a chart though, hence a bar graph can be a line chart.
A plot would apply to line charts, with plotted points. A chart could arrange the data in columns, rows, pie shapes, etc., and plots. Graphs are synonymous with charts, though i would reserve "chart" for more plain depictions and call data arranged in columns of kittens "graphs" (though that's just my style choice).
