A POCO follows the rules of OOP. It should (but doesn't have to) have state and behavior. POCO comes from POJO, coined by Martin Fowler [anecdote here]. He used the term POJO as a way to make it more sexy to reject the framework heavy EJB implementations. POCO should be used in the same context in .Net. Don't let frameworks dictate your object's design.
A DTO's only purpose is to transfer state, and should have no behavior. See Martin Fowler's explanation of a DTO for an example of the use of this pattern.
Here's the difference: POCO describes an approach to programming (good old fashioned object oriented programming), where DTO is a pattern that is used to "transfer data" using objects.
While you can treat POCOs like DTOs, you run the risk of creating an anemic domain model if you do so. Additionally, there's a mismatch in structure, since DTOs should be designed to transfer data, not to represent the true structure of the business domain. The result of this is that DTOs tend to be more flat than your actual domain.
In a domain of any reasonable complexity, you're almost always better off creating separate domain POCOs and translating them to DTOs. DDD (domain driven design) defines the anti-corruption layer (better link here, but best thing to do is buy the book), which is a good structure that makes the segregation clear.