Serendipity versus Coincidence

[S]erendipity is a fortunate or pleasing coincidence. A coincidence need not necessarily always be fortunate.

I was trying to think of 'serendipity' this morning, but I couldn't quite put my finger on it. 'Coincidence' I had, but I knew there was another word with similar meaning that started with an S. Five or ten minutes of mucking about with other stuff and the answer popped up, but now I am wondering what the difference is and why serendipity did not show up as a synonym on the Thesaurus.