The state pattern looks very similar to the strategy pattern; indeed, the UML diagrams for the two are identical. The implementation, too, is identical. We could even have written our states as first-class functions instead of wrapping them in objects, as was suggested for strategy.
While the two patterns have identical structures, they solve completely different problems. The strategy pattern is used to choose an algorithm at runtime; generally, only one of those algorithms is going to be chosen for a particular use case. The state pattern, on the other hand, is designed to allow switching between different states dynamically, as some process evolves. In code, the primary difference is that the strategy pattern is not typically aware of other strategy objects. In the state pattern, either the state or the context needs to know which other states that it can switch to.