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Reaction is something very quick. It inherent without thinking. While responding something is mindfully reply.
The link below might be helpful:
http://jessicadolce.com/react-respond/
Maybe reacting is when one does a quick attribution on a situation.
And responding is when one does a helpful action to offer or do a quick solution.
The difference of the meaning could have occurred culturally, because when I open a dictionary online respond is somehow a subset of react. Linguists know better, am just guessing here.
Responding is acting responsibly in any situation without emotion feeling or reaction.