Are the two adjectives completely interchangeable, or is there a distinction between them?
Does it matter which I choose?
As an adjective 'graphic' refers more directly to the actual process of drawing, or the discipline that has evolved from what used to involve training one how to draw. But 'graphical' refers less directly to drawing as a process, but to the visual result.
As a noun, all depictions are 'graphics', whether drawn or projected.
'Graphic' also has the meaning of 'so vivid you cannot avoid seeing it', as in graphic sex or violence. So people occasionally avoid using it when it can be taken in that sense. (Donkey Kong eating Princess Peach would be graphical violence, but not graphic violence.)
Graphical is used adjective and not as a noun. It is used mainly to mean:
It can be said that "graphic is wider in meaning than graphical.
There is a very technical meaning which might illustrate one of the norms that Wilson mentioned. In mathematics, a graph is a representation of objects where some pairs of objects are connected by links. The adjective form of graph, in this sense, must be graphical.
So to say that a probabilistic model can be represented as a graph, where the objects are random variables and the random variables can be connected by links which represent their dependencies, is just like saying that a probabilistic model can be represented as a graphical model. You cannot use graphic model in this context. (I have heard people say graph model, although that sounds jarring to me)
As adjectives, graphic and graphical are equivalent. Graphic is also a noun, as in a visual graphic, whereas graphical is only an adjective.
However, there are phrases where graphic is conventionally used, other phrases where graphical is the norm. Therefore, it's important to choose the correct word for a given situation.
flowcharts are graphical presentations,
graphical user interface