They are very similar. Sometimes they can mean the same thing. They just seem to have different uses. Mostly, you use "reply" when you are talking about internet communication, like reply to a text, reply to an email, reply to a message. You could say respond too, but it's less common. You would normally say "respond" when you're talking about a reaction, or something you do or say because someone else did or said something first. If someone uses an insult, you might say "I wasn't sure how to respond." Governments always talk about "responding" to the actions of each other. In that context, a "response" can be a bomb, financial, or just words. "response" is also used more than "reply" when describing an "answer to a question." A reporter might say, "we found out this information. How do you respond?" Again, reply still makes sense, but it sounds odd.
Mostly, I think the trick is to learn when English speakers use each word, and in what context. However, if you're unsure, you can just pick one and people will still understand you.
hope that helps!