I would like to get an explanation of the difference between the two arguments, search model and completion model, in the Answers API. Under what conditions one would specify them to be the same (for e.g., curie/curie) vs. different (for e.g., curie/ada)?
The search model narrows down the search space; i.e. just selects which documents are most likely to contribute to a valid answer. This model can be a much smaller one, like ADA or Babbage.
The completion model then takes the smaller set of documents selected by the search model and generates an Answer based on them. This is where the brains are, and this needs to be a more powerful model, such as DaVinci or Curie.
Hope that helps.