My understanding is that you can use either one for that situation because it is a communication or attempted communication of some sort (verbal, written) between people, either directly, or using technology (phone, email, etc.). In other cases when something happens, and there is a non-communication type reaction to it, respond would probably be used.Thanks to all of you for responding or replying? Which one is correct? Or are they both? (in informal American English)
For example, these communication events might take either word.
What was his response/reply when you told him you moved out?
He would not respond/reply to my questions.
She got a response/reply from that company she applied to for the sales job.
Non communication (more reactive) event examples that would use respond only.
How did your car respond to the different gas you're using now?
He responded to the opportunity right away.
He responded well to the medication.
Sometimes though, reply is used figuratively to humanize inanimate objects.
My trusty turbo finally replied halfway down the track as I was about to get passed.
I think it comes down to the situation at hand, and how much etiquette should be involved. If etiquette is important, I might use reply, as it has that human touch to it. But if I'm just sending out emails to people who responded to a survey, I might use respond.