Q: My impression of a DAO is of an organisation (or company) that can exist autonomously. What I'm not sure about is whether a smart contract, or set of smart contracts, be used to define a DAO. If that's the case, isn't a DAO just a smart contract?
A DAO on the Ethereum blockchain is a set of rules implemented as a Smart Contract (or code running on the blockchain). A DAO on Ethereum can hold and release funds based on a set of rules (eg voters approve the release of funds if the project is progressing as promised).
A Smart Contract (or code running on the blockchain) can be used to code the algorithm for a DAO, Pyramid schemes (eg Ethereum Pyramid), lottery and dice games, and other yet-to-be-thought-of things.
See some of the potential uses of Smart Contracts on Where can I find some Solidity / Smart Contract source code examples? .
See The Decentralized Autonomous Organization (DAO) - A Primer for some information on DAOs.
EDIT 27/04/2016 - From Smart Contracts Described by Nick Szabo 20 Years Ago Now Becoming Reality:
Szabo defined a contract as being “a set of promises agreed to in a meeting of the minds [which] is the traditional way to formalize a relationship.” Such contracts are a pillar of a free market economy and can be useful in business relationships, marriages and politics.
Smart contracts would improve execution of the four basic contract objectives, which Szabo described as observability, verifiability, privity and enforceability. Among other use cases discussed in the following sections, smart contracts according to Szabo would enable both parties to observe the other’s performance of the contract, verify if and when a contract has been performed, guarantee that only the details necessary for completion of the contract are revealed to both parties and be self-enforcing to eliminate the time spent policing the contract.