I think the term "smart contract" is a misnomer. Sure, you could write a code similar to one I use:
Store money and confirm that I am alive every year (by means of me sending a transaction to the contract). If I don't send this transaction, all money is released to my daughters account. This looks like a standard contract.
Now, dApps (distrubuted applications) also use "smart contracts" as the backend, but they do so much more than act as "contracts". For example, Golem is a computation market, Augur is a prediction market, etc. There is a whole universe of applications that can be written on Ethereum that do not quite fit under a simple "contract that you can write using a lawyer and some pen and paper" umbrella.
Now, dApps (distrubuted applications) also use "smart contracts" as the backend, but they do so much more than act as "contracts". For example, Golem is a computation market, Augur is a prediction market, etc. There is a whole universe of applications that can be written on Ethereum that do not quite fit under a simple "contract that you can write using a lawyer and some pen and paper" umbrella.