"Notion" and "conception"

Solution 1:

According to The Free Online Dictionary, here is a comparison of synonyms of idea:

Synonyms: idea, thought, notion, concept, conception

These nouns refer to what is formed or represented in the mind as the product of mental activity.

Idea has the widest range: "Human history is in essence a history of ideas" (H.G. Wells).

Thought is distinctively intellectual and stresses contemplation and reasoning: "Language is the dress of thought" (Samuel Johnson).

Notion often refers to a vague, general, or even fanciful idea: "She certainly has some notion of drawing" (Rudyard Kipling).

Concept and conception are applied to mental formulations on a broad scale: You seem to have absolutely no concept of time. "Every succeeding scientific discovery makes greater nonsense of old-time conceptions of sovereignty" (Anthony Eden).

Solution 2:

One can have many notions about a single concept but a notion usually cannot be about many concepts.