There are two basic concepts that I understand separately, and that are often explained in articles about space imaging. The first one is that the wavelengths (colors) of light seen in an image can be used to determine what chemical elements are present at the source, because different elements emit or reflect different wavelengths. The second is that the Doppler effect causes light emitted from sources moving away from the viewer to appear to have longer wavelengths, or become "red-shifted", and light from sources moving toward the viewer to appear to have shorter wavelengths, or become "blue-shifted".
I understand both of those concepts separately. But now my question is... When given an image, which shows data about brightness at specific wavelengths of light observed from our solar system, how can a scientist tell whether the wavelengths indicate the presence of one element, sitting still relative to us, or some other element, moving toward or away from us?