Back when I was in college for the fine arts, my instructors and peers used to use a general term for all surfaces an artist would paint or draw on. I recently became active on the Arts & Crafts stack exchange, and suddenly discovered that, having not spoken about art in a technical way for many years, I have forgotten this word. As a result, several of my answers there have very awkward phrasing to skirt the subject. The diversion is intrusive and reduces the quality of my answers, and I worry it may cause them to be misleading.
A similar term would be "matrix" in printmaking, which refers to any block, plate, stamp, etc., which will be altered to create the final image. It covers a wide variety of materials and techniques to refer to them all collectively by their common purpose. It does not, however, refer to the images they make or the surfaces they mark. (The image is a print, the surface is… the word I forgot)
Since I graduated, the college I went to has replaced all of their arts instructors, so I don't really have any contacts there any more. The one class mate I'm still in contact with says he never bothered with that anyways because he didn't want to be a draftsman or painter, so it didn't apply to his goals. None of my textbooks go into that degree of depth in technical language. Only one book has a glossary, and it is aimed at a much younger audience, defining things such as "pencil".
Best Answer
My first instinct is the word medium, which is a catchall. Alternatively, the word support is more specific.
It's important to realize that while "support" is a closer fit, it's rather obscure. For a general audience (and I think A&C counts as general), I would use the word medium.
Here's a quote that goes into some of the technicalities: