I can't say I am a Geologist, but I have some knowledge. It looks to me as if the vein has filled and then re-dissolved during its lifetime, which would fit with a Calcite or Gypsum intrusion. It looks more Gypsum to me. A few answers might help:
1. Whereabouts was it found initially? Was it in a river or the sea when found? Or exposed to rain?
2. How hard is the grey rock? Does it scratch with steel, or a finger nail?
3. Have you tried the drop of vinegar on the white crystals yet?
However it got to where it is, it looks really cool!