I had the same question too. The footnote #1 states that >"StackEdit is a free, open-source Markdown editor based on PageDown, the Markdown library used by Stack Overflow and the other Stack Exchange sites."
Based on the same library that another website uses doesn't warrant the use of a similar logo though. It was confusing to the point of "Oh look, a StackOverflow button, I wonder if it posts to StackOverflow"