What's the exact difference, if any, between a Wiener and a Frankfurter sausage?

Not really any. Although some sources suggest that there is a difference in size, different manufacturers' versions of the same thing differ as much as the reputed difference between wieners and franks.

Wieners get their name from Wien, or Vienna, the Austrian city from which they originate; Franks were developed in Frankfurt, Germany. Both are often simply referred to as hot dogs. Neither should be confused with the Vienna sausage, which is an entirely different beast.
http://www.wisegeek.com/what-is-the-difference-between-a-hot-dog-weiner-frank-and-sausage.htm

Sausages vary from region to region. The differences may be marked or subtle.
The Vienna sausage is a weiner. Weiner stands for Viennese in German.

The Viennese will trace the lineage of a hotdog back to the Weinerwurst or Viennese sausage. The Germans on the other hand to the frankfurter Wurst.
The hotdog sausage is called both a weiner and a frankfurter. Frankfurter is linked to Frankfurt, Germany whose people lay claim to having invented the hot dog. But, in all German speaking countries (except Austria) the sausage is called a weiner.

https://en.wikipedia.org/wiki/Vienna_sausage

https://en.wikipedia.org/wiki/Frankfurters

A person from Vienna is called a Wiener, not a Weiner.
The sausage in Deutsch is called Wiener Würstchen.

http://de.wikipedia.org/wiki/Wiener_W%C3%BCrstchen