Vinegars have been making themselves out of wines and other alcoholic beverages for thousands of years — it is a natural process in which bacteria in the air combine with the alcohol and turn it to acetic acid. But you needn't start with wine or grain alcohol. Nowadays, vinegars are commercially made from a wide variety of fruits and grains. In fact, any liquid containing either sugar or starch can be caused to ferment and become a vinegar.
Rice vinegars are made from fermented rice. Rice wine vinegars are generally made from the lees (dregs) of the wine. Both and widely used in Asian cooking. Both, especially those from Japan, tend to be mild and sweet, and add a bit of acidity to dressings and in cooking. The Chinese red and black varieties are also used as condiments, but still are characterized as mild vinegars. There are also Korean varieties, some of which are much stronger.
Although Haggis isn't technically correct in saying that "rice wine vinegar" isn't made from rice wine, I do agree with him that rice vinegar and rice wine vinegar are essentailly the same thing and entirely interchangeable in most any recipe.
In order to convert rice (or fruit or other grains) to vinegar, it must be converted to alcohol before it's converted to vinegar. So, in essence, it starts as rice, becomes rice wine, and then becomes vinegar.
You can also take a bottle of a grain or fruit that has already been converted into alcohol (eg, sake, champagne, sherry, red wine, cider, etc.) and convert that into vinegar.
So, really, "rice vinegar and rice wine vinegar" are the same thing.
To further confuse ... there are various products in asian stores labeled as "rice vinegars" that actually began as rice wine or the end=product of sake. My local asian store carries maye 40 differnt kinds of rice vinegar.
Chinese rice vinegar usually comes in 3 types: black, red and white. Good black vinegar ("Chinkiang ") is sweet and often used as a condiment.*
Japanese rice vinegars are nearly all white and colorless.
The sweetness, taste, acidity, etc. are both a function of the type of vinegar and the quality of the manufacturer.
Rice wine vinegar and rice wine are not the same thing, obviously.
* Those of you near NYC will have had this if they enjoyed Joe's Shanghai soup dumplings