Why would the digital optical output from my CD player be louder than that of my streamer?

I thought that a digital output audio signal didn't have volume info encoded in it; ie, that the bit depth tells you the dynamic range of recorded sound, from 0 to highest volume, but does not tell the downstream devices how loud the sound should be (ie, what you actually hear, in SPL).  In other words, the volume would be entirely determined by the preamp (after the DAC converts it from digital to analog), not by the digital output source.

 

But I'm finding that the digital (Toslink) output of my Cambridge CD player is noticeably louder than that of my Bluesound Node, after going thru the same DAC and preamp. Is my assumption of the digital signal having no volume info wrong?