Emulation is when you are replicating, in a different system, how the original system actually internally works considering each function and their relations.
Simulation is when you are replicating by the means software, the general behavior of a system starting from a conventional model.
The difference between valaidation and verification is the process of checking whether the specification captures the customers needs, while verification is the process of checking that the software needs the specification.
Certification is refers to the confirmation of certain characteristics of an object, person or organization.