Starbound is from a different developer, only one person worked on both games. Starbound is quite similar to Terraria, but there are a few key differences such as races, you can go to an infinite number of randomly generated planets(selling point for me lol), and the world doesn't end, it wraps around (planets are round, you can walk in one direction and end up where you started).
Starbound is not a sequel, but many people call it a spiritual successor to Terraria. It's almost like a High Quality mod of it to me.
Both games share key similarities but Starbound has more of an emphasis on questing and NPC interaction. Terraria does to an extent but its mostly about surviving, which is my preferred gaming style.