The 'Harvest Moon with a Dark Story' might refer to a work of art, like a painting or a piece of literature. In a painting, the artist could have depicted the harvest moon in a spooky or ominous way, with dark shadows and a desolate landscape below it. In literature, a story could be set during the harvest moon time, where there are dark secrets, murders, or other sinister events that unfold under the light of the harvest moon.
In European folklore, there are tales of the harvest moon being a time when witches were more active. The 'dark story' could be about how they would steal the crops or cause harm to the farmers. For example, in some regions, it was believed that if a black cat crossed your path during the harvest moon, it was a sign of impending doom related to your harvest.
No, they're not the same. Story of Seasons is a new series that developed from the Harvest Moon franchise but has some distinct features and gameplay differences.
They aren't identical. Harvest Moon was the original, and Story of Seasons is a continuation with its own tweaks and improvements. The worlds, quests, and overall feel can vary between the two.