Was Bretton Woods a real gold standard?

There are many differences between Bretton Woods and the classical gold standard of the 1800s. My claim is that despite these differences, for a short period of time the Bretton Woods system did everything that the classical gold standard did. I'm using David's definition of a gold standard whereby the monetary unit, the dollar, is tied to a set amount of gold. This linkage ensures that there can never be an excess quantity of monetary liabilities in circulation—unwanted notes will simply reflux back to the issuer in return for gold. When most people criticize Bretton Woods, they say that it lacked such a linkage.

Was Bretton Woods a real gold standard?