When used for measuring ingredients in cooking what is the difference between a "dry ounce" and a "liquid ounce"?
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.