Most people don't really understand that.
Even relatively informed people don't understand that physicians aren't members of the scientific class and in practice are closer to car mechanics than fuel chemists.
A person with a DMA, DPA, or a DMM are all still called "Doctor" colloquially, but not people with a JD.
A Doctorate of Science should by the sound of it be the one that members of the science class have, not a PhD, but it curiously represents both an award that's equivalent, beyond, and less than a PhD depending on who awards it and how it's awarded -- and is curiously often the degree of choice for medical doctors and other health practitioners but almost never the degree for chemists, biologists, physicists or other sciences.
Most people don't even know there are doctorate degrees other than PhD.