This is discussed extensively here: Save volume rendering as STL file - #14 by maxabernathy. In short, volume is saved as is (with single-component scalar values) and you color it using transfer functions (scalar opacity transfer function, scalar color transfer function, and sometimes also gradient opacity transfer function). Transfer functions are saved in a .vp file when you save the scene (simple text file that list number of points in the transfer functions, followed by the point coordinates). You can find information about these transfer functions and how they are used for volume rendering in VTK textbook.
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