I've seen numerous recipes that call for measuring "liquid ounce" but at the same time telling you to measure something like flour as "dry ounce" - I've even seen references to "fluid ounces". Are they interchangeable when measuring ingredients? If not why, if so why separate the two types of measurements?
Both liquid ounces and fluid ounces are the same. They are a measure of volume. These are commonly called liquid measurements. These include: teaspoon, tablespoon, fluid ounce, cups, pints, quarts, and gallons. Why fluid? Because it's measuring volume.
The term "dry ounce" is one I have never encountered. It's rather confusing and misleading. Technically a dry ounce would imply a measurement of weight. 1 oz = 28g.
Your recipe could be calling for a measurement by weight of flour, or it could be using a terrible phrase "dry ounce" to imply that you should measure the flour with a measuring cup used for dry measure, as opposed to a measuring cup used for liquids.