Scratch paper, to me, is specifically for the preliminaries of something which is going to be fair-copied or otherwise produced in finished form later. It's the paper you use for first drafts, for the arithmetical calculations you need to finish your calculus exam, for the initial notes to the speech you're going to give. That kind of thing. A phone message or things like that, where the note form *is* the finished form and it needn't be improved, would go on scrap paper, which is a broader category and includes any paper that's in bits and oddments, whether or not it's going to be written on (wrapping paper oddments can be scrap paper too).
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