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.