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" a strident confidence in one's judgement about some matter that's out of proportion to one's actual knowledge and experience."

vs.

"childish optimism that one can take on any challenge."

So is age the only differentiating criterion?

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No. There's an important difference in tone or attitude and also in content. "I have little to nothing to learn about/from this" vs "I can [will be able to] do this". Kids can be arrogant and they can be childishly optimistic. Programmers are notoriously optimistic about our ability to quickly solve problems, but even where it's not arrogance (as I think it's usually not) I wouldn't usually call it childish optimism since (1) it has lost it's charm since more is usually at stake and (2) we expect people to grow up and do better than they did when they were nine.

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