Mr. Rewrite did a spit take when he read this line in an article today: "It hopes this will staunch the Post's estimated $50 million in losses." That's because Mr. Rewrite is a staunch supporter of keeping staunch and stanch straight.
Yes, gentle reader, these spellings are indeed variants of each other. But it doesn't take a purist to point out that stanch should be used when referring to stopping the flow of something such as bleeding, be it literal or figurative.
Staunch should be used for the adjective meaning steadfast.
The Associated Press Stylebook is just one of the reference books backing Mr. Rewrite on this point. That makes it interesting to follow these links to see how many of those with editors botch stanch/staunch: