As has been discussed in comments:
The exact sizes of these measurements vary by country and by historical period, as can be seen at the links.
The fact that these units have a similar name is due to historical accident, and you'd be better served by not thinking of them as related AT ALL. They simply measure different things.
In a recipe, the word "ounce" is ambiguous. Unless the recipe or source specifies, I would generally assume:
- An "ounce" of anything liquid or roughly fluid (gravy, sauce, syrup) should usually be measured in a measuring cup by volume (regardless of weight).
- For dry goods, usually an "ounce" refers to weight, not volume.
- Recipes for baking sometimes also include weight measurements in addition to volume measurements (e.g., cups); in this case it is generally clear that an "ounce" refers to weight measurement.
- Professional cookbooks for large quantities sometimes have recipes which are entirely given in weight measurements; again, in the case context should make that clear.
To answer the question about why we use a "fluid ounce" rather than other volume measurements, originally the "fluid ounce" referred to a volume of a specific fluid that weighed an ounce, usually wine, ale, or water. An "ounce" would thus be a different size depending on the substance being measured. A couple centuries ago, both the U.S. and Britain decided to standardize the "fluid ounce" as a volume measurement equivalent in all contexts, regardless of the substance. Britain chose water as its standard; the U.S. chose the old British wine measure as the standard size for its ounce. Regardless, all fluid ounces are now defined as having a particular volume, with no necessary relationship to the density or weight of the material.
Despite the confusion it causes, the name stuck. For some reason it become adopted as a standard volume measure, probably due to its size and standardization. (Pints were too large and potentially inaccurate for labeling consumer goods; drams and minims were useful for pharmacy but were too small for labeling volumes of any size. Intermediate units like tablespoons and cups tended to vary in size historically. And no one seemed to like using the gill outside of alcohol measures.)
More details on use below.
To clarify a previous answer: If the term "dry ounce" occurs (only generally in culinary contexts), it is ambiguous and could refer to:
- Measuring something as an ounce by weight (1/16th of a pound)
- Measuring a solid -- usually a powder, finely chopped materials, or a semisolid like butter -- using a fluid ounce volume (1/16th of a liquid pint, equivalent to 2 tablespoons)
Large quantities of dry goods in the U.S. are measured in bushels, pecks, dry quarts, and dry pints (which are about 16.4% larger than liquid pints). A "dry ounce" (as 1/16th of a dry pint) is NOT used as a volume measurement. (They definitely don't exist officially in the U.S., which is the only place that still has "dry measure" volume units.)
There's no reason for it to exist. The dry pint is the smallest official unit of dry goods; the FDA does not acknowledge the possibility of "dry ounces" for food labeling (see regulation 101.105(b)(3)). Anything solid smaller than a dry pint must be measured by weight or using fluid volume measurements. Smaller units in culinary purposes (cups, tablespoons, teaspoons, and yes, fluid ounces) are all liquid volume measurements which are derived from (and equivalent to) the liquid system, not related at all to the dry goods units.
Also, while we're clearing this up, contrary to popular lore, a "pint is NOT a pound the world around," even with water. In the traditional Imperial system, a fluid ounce of water does weigh exactly an avoirdupois ounce. But an Imperial pint is 20 ounces, not 16, so a pint weighs more than a pound (1.25 lbs., actually). In the U.S. customary system, the fluid ounce was defined as 1/128th of a wine gallon. Thus, a fluid ounce of wine should weigh approximately a U.S. ounce. But since water is denser than wine, a fluid ounce of water weighs more than an ounce (by weight); similarly, the U.S. pint of water (16 fluid ounces) weighs more than a pound (about 1.044 lbs.).
For that matter, the other place of confusion occurs with butter, which is assumed to have 16 ounces in a pound, according to the way each stick is generally marked in the U.S. (with 8 tablespoons = 4 (fluid?) ounces). But butter is about 5% less dense than water and 16 fluid ounces of butter can't weigh the same as 16 fluid ounces of water. A pound of butter thus usually contains somewhere around 33-35 tablespoons, despite being marked as containing 32 tablespoons. This discrepancy is usually not significant in culinary practice and also applies approximately to oils. (To add to the confusion, a U.S. tablespoon for labeling purposes is often defined as 15 milliliters, rather than the 14.787 milliliters which actually make up 1/2 of a customary U.S. fluid ounce. A fluid ounce is also therefore defined by the FDA in the U.S. to be 30 milliliters when referring to nutritional information -- see point 9 here.)
Anyhow -- other than for butter/oil and water/wine, though, these sorts of relationships between volume and weight measurements don't hold AT ALL.
In general, I would avoid trying to equate these two units in any meaningful way, since they only relate in very specific cases and only imprecisely even then. A fluid ounce refers to volume (and is related to cups and pints and quarts and gallons and liters); an ounce is a measure of weight (and is related to pounds and kilograms).
For culinary purposes, it's simple:
- if you're using a cup to measure something, you're measuring volume (fluid) ounces (whether the material is liquid or not)
- if you're using a scale, you're measuring ounces
- if you're measuring butter or shortening in a stick, just accept what the package says and don't think too hard about it