There are a lot of differences between the two games.
- Races that are not Human - Starbound has 6 playable races, with a seventh to be released in the future.
- Space Exploration - You are not limited to exploring one planet in Starbound. In fact, as soon as you have the fuel you need to pilot your spaceship (coal), you can leave your starting world and explore any planet you want.
- Very Different NPC Interaction - You will sometimes come across NPC generators that will create merchants, doctors and other NPCS that act like Terraria NPCS, but for the most part, NPCS are found on worlds, and can be hostile or non-hostile, offer merchant services, and are remarkably chill about you looting their house for all its valuables but VERY touchy about you holding a sword.
- Different Mining System - You can mine much wider spaces in Starbound, especially once you get a pick (the multitool is useful, but weak).
- Survival Mechanics - Unlike in Terraria, you actually have to eat regular meals and keep warm, or you will die. Heat sources are easy enough to craft (though you'll need better ways to stay warm on colder planets), and food can be a little troublesome to come across, but it is an interesting challenge nontheless.
Of course, there is one very key difference right now between Starbound and Terraria that is very important to consider.
Starbound is still in Beta
And it's still a somewhat buggy Beta, with clipping issues and game-format-changing fixes and patches being applied as the Beta progresses. There is a certain 'unfinished' feel to it right now. Whereas Terraria has had years and years to not only be a fully released and finished game, but to have numerous patches, updates, and content additions added onto it, making it much more polished and mature.
So if you are still interested in Starbound, keep in mind that it is still in Beta, and still in the early phases of being improved. A lot of the "higher tech" content that will set it apart from Terraria has not really been implemeneted yet (there are very few blueprints, very few high-tech crafting recipes, and what is there is still being improved upon), but it is forthcoming.
There are a few other minor differences here and there, but these are some of the more major differences between the two games.