Conceiving is the process of arriving at an idea. For example, If there were no artificial light in the world, one might conceive the need for some form of electric torch. That would be conceiving. But the design of an actual incandescent bulb versus a fluorescent one would require conceptualizing a specific implementation of the idea one has conceived.
Conceiving need not come before conceptualizing. For example, a common dramatic technique is to give a character a very clear mental image of an object or arrangement that holds the solution to the story’s problem. But the character does not know the solution lies in the conceptualization. It is only when it finally conceives of the need for a particular kind of solution does it realize it had the answer all along.
Simply put, Conceiving defines the question, Conceptualizing clarifies the answer.
The Zen of Story Structure
DEFINITION: Conceiving: coming up with an idea.
SYNONYMS: originating, inventing, devising, engendering, hatching ideas.
DYNAMIC PAIR: Conceptualizing, visualizing how an existing idea might be implemented.