It is not briarwood. There were hundreds/thousands of these made and the wood had to be plentiful, cheap, and easy to burn with a hot tip. When I have more time I will take a couple of mine, a loupe, and my wood book and see what it is. Top guesses are ash, poplar, basswood, and gumwood.
Wikipedia says..."Light-coloured hardwoods such as sycamore, basswood, beech and birch are most commonly used, as their fine grain is not obtrusive, and they produce the most pleasing contrast. However, other woods, such as pine or oak, are also used when required."
http://en.wikipedia.org/wiki/Pyrography