Differential evolution is actually a specific subset of the broader space of genetic algorithms, with the following restrictions:
- The genotype is some form of real-valued vector
- The mutation / crossover operations make use of the difference between two or more vectors in the population to create a new vector (typically by adding some random proportion of the difference to one of the existing vectors, plus a small amount of random noise)
DE performs well for certain situations because the vectors can be considered to form a "cloud" that explores the high value areas of the solution solution space quite effectively. It's pretty closely related to particle swarm optimization in some senses.
It still has the usual GA problem of getting stuck in local minima however.