Even after story was added to the game in Minecraft, it allows you to play at your own pace a lot more.
Each stage of the game you trigger in Terraria, it gets more difficult, and new threats arise on the map. If you’re not upgrading all your gear in the designed paths, you’ll be suffering and dying a lot.
Minecraft doesn’t do that so much. It lets you choose which things you want to work on, or if you even want to work on them at all. There’s nothing stopping you from just deciding to build an idyllic cottage and not pursue a path to the Ender Dragon or anything else.
Terraria kind of pushes you along, Minecraft doesn’t and lets you play at your own pace. Definitely for different types of gamers, in some ways.