"React" and "respond" are synonyms.
The quests and power-ups that talk about reacting instead of responding make no sense at all. "Respond" actually has the word "react" in its definition, and "react" has as its verb's definition "to act or respond."
In terms of cognitive stuff, though (like people with depression or anxiety), a 'reaction' is often more reflexive and closed-off, whereas a 'response' is taking a moment to think, internalize something, and then really engage with what you're responding to.
They are different in psychological jargon, if not in the standard Webster's definitions.