They can be synonyms. We can say, equally well, "Frank Lloyd Wright had an impact on US architecture" or "Frank Lloyd Wright had an influence on US architecture." They mean almost the same thing. "Impact" is a stronger word. It suggests a sudden, strong effect--like a physical impact, like a hit or a blow. It comes from a Latin root meaning "to push against." "Influence" suggests a gentle, weaker, slower effect. It suggests guiding a flow, and gently directing it into a new direction.

I think we would have to know the context to answer this. However, if the context is something like: "your answer will impact my decision", or "your answer will influence my decision" - then the two words have the same meaning. There are contexts where the words will have different meanings, though.