As mentioned before, Terraria is a little like Minecraft crossed with a 2D platformer or more specifically with a 2D Castlevania game. (And given both the name and the also aforementioned graphical similarity to SNES era FF games i decided to name my character "Terra" and design her to match =)
In a more general sense however, Minecraft is a game with a little bit of gameplay and a lot of building, while Terraria is a game with a little bit of building and a lot of gameplay.
In Minecraft there are very few monsters and you're going to spend most of your time building stuff. You encounter at least 75% of the practical stuff you need in the first couple hours. The only stuff you have to work very hard for are Diamond, Redstone and Obsidian, and even those aren't really necessary for most things. You can (and people have) built massive, impressive and beautiful things using only substances you can acquire within a few meters of the surface. You'll quickly exhaust the "game" part but can be entertained by either building your own stuff or seeing what other people have built
In Terraria there's not much to building stuff (at least i haven't found it very interesting so far.) You certainly can effectively create anything you want, but the end result looks like any other bit of 2D art. Perhaps i'll get inspired later, but so far i haven't gotten impulses of "I wonder if i could build an [x]" or "That's an awesome landscape over there! I bet it would be even cooler if i built an [x] on it!" I also can't currently imagine wanting to see YouTube videos of what people have created, or even bothering to skim through a picture gallery. Perhaps that will change after i've played they game longer, though if it does i'll certainly be surprised by it.
What Terraria does have in abundance however is gameplay. You encounter slimes right away during the day as soon as you start the game, and i died once or twice from them before i figured out the right tactics to handle them. Then when night comes out zombies and flying eyeballs appear. Wood, earth and stone are pretty easy to acquire but even getting just enough copper or iron to forge decent armor and weapons can be a challenge early on. It's a 2D world so you can see ore deposits underground and inside walls (assuming there's a sufficient light source) but those deposits are scattered much more widely than in Minecraft, and you need a lot more of the material. Crafting in this game is pretty much just a purchase system. You don't have to arrange anything in a tiny grid or discover recipes, if you've got the items and the right crafting tool then the item will show up for "purchase" as soon as you open the crafting menu. Which is good since without a crafting table like Minecraft there's no limit to how many ingredients something might require. Higher level items can require dozens of pieces of three or four (or more?) different kinds of components.
If you travel far enough away from your starting point you will eventually discover the "Corruption", which i'm told looks like it's covered in purple grass. I've never gotten that far yet because when you get close to it tougher monsters start spawning, So far i've encountered harpies and some kind of larger undead eyeball thing. Likewise as you dig deeper underground you discover tougher monsters, though i haven't gotten anywhere near deep enough to discover most of those yet.
Terraria doesn't follow the semi-realistic materials scheme of Minecraft. Anything made out of silver is better than the iron version, and gold is better than silver, and there are several more categories of materials above gold which are even harder to get. Delving deep enough to the hell layer will allow you to collect one stronger material. And also stronger monsters. There's a way to trigger a giant meteor strike which will bring with it a stronger material. And also stronger monsters. There are ways to summon giant boss monsters. Which drop a stronger material when killed. You can level up your character's stats a little by acquiring Heart Containers (increase max HP) and Star Containers (increase max MP) but all the other stats are based on your equipment. So it's pretty much like a normal RPG, get better equipment/levels so you can fight stronger monsters so you can get better equipment/levels.
After about 15-20 hours i've got mostly silver and gold equipment and am wondering if i should spend some time grinding for heart containers, go check out the Corruption, or try digging down to the Hell layer. I'm sure someone who knew what they were doing right from the start could do a lot better than that. On the other hand i've been making fair use of the wiki and checked out the map of the world a couple times to figure out where good concentrations of goodies are, so someone starting out new and trying to do it completely blind might have even more difficulties.
Speaking of which, when i started the game i decided to create a "Large" world, because larger is always better, right? ;) Then i tried looking for some of the floating islands i'd heard about. After having some difficulty with that i tried out one of the map creator programs and realized that large worlds are LARGE. And after checking out the wiki a little more i found that large worlds have about four times the area of small worlds but do _not_ have four times as many resources.
I'd strongly suggest that anyone trying out the game start with a small world.
Also, if you want to skip ahead a bit then try building a sky bridge at about 80 blocks down from the top of the world and see if you can find any floating islands, it could potentially save you a lot of the early grinding for copper and iron :)
And as long as i'm offering advice, here's a quick link to the Terraria Wiki for anyone who's not feeling masochistic enough to figure out everything themselves. (And which itself has links to the map creators under "Tools" if you're feeling really lazy =)
So i'm definitely having fun with the game and there's certainly a lot more of it go, but i'm not sure what will happen once i've built some of the best gear and beat most of the boss monsters. I've gotten distracted from Minecraft multiple times and come back multiple times because there's always something new to try and build (or watch on YouTube.) I'm not sure if there will be anything in Terraria to draw me back after i'm "done" with it. But of course that makes it pretty much list most other games that aren't Minecraft and don't have competitive multiplayer :) And at $10 for one and $20(?) for the other it's not like getting both Terraria and Minecraft would be a huge financial burden for most people.