Algebraic effect handlers and delimited control operations are abstractions of computational effects. Originally proposed without labels, their labeled extensions can express multiple kinds of exceptions, multiple states, and so on. We show that the two abstractions have equal expressive power. To do this, we first develop a type system for each abstraction with each label extension. We then define macro translations between two abstractions with the same label extension. The equivalences establish a strong connection between the two abstractions with labels, which can be used to understand and implement one abstraction in terms of the other.