The double flowered stock is the same species as the common garden stock or gillyflower. It is simply a variety with extra and overlapping petals, which makes for very decorative and full-looking flower heads.
The double flowered characteristic is one of the oldest abnormality observed in flowers, as it was already mentioned in ancient Greece. Double flowered varieties are often sterile and must then be propagated through cuttings.
The caption reads in the original French: