They are definietely different.
Terraria has different biomes, enemies, other kinds of items to craft/find (no minecarts or boats, but there are muskets, chandeliers and grappling hooks. That's just to name few.).
Terraria is more fast-paced, and resources are bit easier (in my opinion) to find/gather than in minecraft.
Terraria has more kinds of minerals/materials, yet you can't make pickaxe out of diamond.
Terraria has NPCs that talk and even sell stuff / cure your wounds.
Minecraft has wolves.
Terraria has depth meter; Minecraft has maps.
Terraria has bossfights. Minecraft has portals to the nether. (Terraria does have "the underworld", yet you can just dig to it, instead of making an obsidian portal)
And, as far as I know, Terraria has a bit more items than Minecraft, including all the raw materials. And magic.
...I guess I could point the differences for quite a long time. Also, in Terraria, sand is OP.
Just don't start a "Minecraft / Terraria is better" war. They are different. No better/worse factor. Really.