I'll go ahead and get this out of the way. The similarities are immediately visible the second you hop into a world, so I won't bother dancing around them, Terraria is very much like a 2D Minecraft. But don't think of it as a complete rip-off. It takes many good traits from MC, yet shapes their own unique spin on a successful formula.
Terraria can be just as addictive as MC, though maybe for a different reason than you think. I, myself, found myself searching more for ores and special items to improve my armor and summon bosses, which in turn dropped better stuff to help craft better armor. In MC? Different story. Mostly building.
Terraria is more goal-based, though it still lets you take whatever path you want, be it improving your armor or working on a better, more efficient house. The game focuses more on adventure than building, however.
As much as I enjoy MC, Terraria rewards you so much more for adventuring than Minecraft ever has so far, boasting SO much more variety.