How are evolution and variants of aircraft considered by certification authorities?
Variants are seen as a modification of an existing airplane design, and only the changed parts need to be certified. The real advantage is that the set of rules the certification has to comply with are frozen at the time of the initial application, so any additional rules that had been added later are not relevant. This is called "grandfather rules".

This definitely lightens the certification process and makes it less complex, but makes the safety enhancements, which were added after the type was certified first, optional for newly built airplanes. 

The A318, A319 and A321 are all variants of the original A320, and the subtypes you name differ in their engine. Each engine option has to be certified separately, but all certification work not related to the engine can be shared between the variants. Additionally, the purchaser will select his options for instrumentation and furnishing, chosen from a limited set of previously certified options.

When a new version is introduced, the public will get a very different message from the airplane maker than the certification authorities. For the PR, the new variant is all new, but the FAA and the EASA will hear that almost nothing changed. In the end, it is similar to corporate profits: The shareholders get told the company made oodles of money, while the tax authorities will be presented with a bleak picture of mainly losses.