Hans, thanks for summing that up so tidily, and to Rich for the elaboration.
Don, you are incorrect about turpentine, but you are correct about Turpenoid starting out (and perhaps still being) a brand name of a turpentine substitute.
However, the most common paint solvent isn't any of the above—it's water.
The most common solvent for enamel paint is not turpentine, either, it's primarily mineral spirits. Some "paint thinner" is a blend of mineral spirits, toluene, and xylene, and sometimes other solvents.
If the paint thinner you are buying is cloudy at room temperature, it's probably pretty crude stuff. I'd recommend switching to odorless mineral spirits. You're less likely to get an unpleasant surprise.
Yes, I was a paint chemist.