When reading about volume rendering, I see voxel rendering is mentioned a lot. I know volume data have voxels, but are the two terms interchangeable, or are they completely different?
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They are not interchangeable, but neither completely different. As your question title says, voxel rendering is a form of volume rendering, as it renders a volume. You can visualize volumetric data with a variety of methods, voxel rendering being one.
EDIT: You should also beware that sometimes people use the term volume rendering for algorithms that just render a set of discrete volume elements (voxels) and therefore really interchangeably to voxel rendering. But sometimes use it to refer to the more general visualization of 4 (or higher) dimensional data (as it arises e.g. from medical or geographical imaging precesses), which is rarely done by traditional voxel rendering (rendering small “boxes”).
You should not use volume rendering and voxel rendering interchangeably, as the former is a much broader and more general topic.