You're right, those two locations are connected!
* Deep Dark Crater is a dungeon found in the post-game of Explorers of Sky.
* The Same Things is a location mentioned within the Deep Dark Crater, specifically in the final chamber.
While the Deep Dark Crater is a physical location, "The Same Things" is more of a concept. It's the name given to the entity that created the crater and the otherworldly beings that dwell within it.
So, to summarize:
* Deep Dark Crater is a physical dungeon you explore.
* The Same Things is a concept referring to the entity and beings that inhabit the crater.
I hope this clarifies things! If you have any other Pokémon Mystery Dungeon questions, feel free to ask!