How does recognizing an answer differ from creating an answer to a question? What are the scientific terms to use when researching the difference between the brain abilities demonstrated in recognizing an answer (e.g. multiple choice) versus creating an answer (e.g. fill in the blank)? 

I just blew through a new Lumosity recognition game and yet struggled with a familiar fill-in game. I'm curious which cognitive abilities are involved. Naive Google searches brought me back a lot of "recognizing creativity in the workplace" type answers.
If I understand you correctly, then the terms you are looking for are "recognition" and "recall".

See: http://www.ehow.com/info_7754397_recall-vs-recognition.html

In depth:


https://en.wikipedia.org/wiki/Recall_(memory)
https://en.wikipedia.org/wiki/Recognition_memory