Hi robsteveson,
Dunlop and Dunlap are the same thing. Dunlop is the most common name and the “correct” one but there are many people who also refer to it as Dunlap. I don’t know where the original misspelling originated or why it because popular.
You can read a little more about the different types of latex in post #6 here. All the latex you are likely to encounter (Dunlop or Talalay production methods using either blended or 100% natural latex) has been certified through various testing organizations such as Oeko-Tex as being free from harmful materials or VOC’s and latex in any of its many versions is one of the “safest” materials available.
The choice between Talalay and Dunlop is really a matter of personal preference (you can read a bit more about the differences in how they feel in post #7 here although personal experience would be the best way to know which one you prefer.
Phoenix