Hey Michael!
The hazy head is referring to the CLARITY and/or TRANSPARENCY, or lack thereof, on the bottom/resonant snare drum heads that different compnies offer today. The Remo heads are almost ALL hazy, as in: You can see through them, but not clearly. The Aquarian's are crystal clear... like looking through glass. Ludwig heads are crystal clear. Attack heads were crystal clear back when I was using them... but I haven't played those in many years so I don't know if they are different now. And so on...
Have a look at your resonant/bottom snare head. Depending on brand, it may be CLEAR... or HAZY. The mil thickness of the mylar is pretty standard though, company to company, although I'm sure there are exceptions here and there. Regardless, resonant/bottom snare side heads aren't very thick, they have to be thin so they will excite easily when moved by the air column after the drum is struck.
Tommyp