When I used to teach English to Japanese high school students, I always tried to get them interested in etymology—the story of meaning. If you know where words come from, you know how they are related and how they're different. I always taught reply, reflex, reflect, and replicate. Today, I’ll throw respond in, too.
Reply and respond seem the same; they both mean a type of answer. But their histories tell a different story. Respond comes from re- (back) and spondere,1 to pledge. A response is more than a reply, it is a promise. First responders do more than reply in an emergency: they respond by showing up and taking action.
A reply, in contrast, comes from plicare: to fold. While a response is a pledge back or a promise in return, a reply is a folding back. In the 14th century, ply made its way into English (via French), as a verb meaning to bend. This is what a pair of pliers is for.
In the 1530s, the noun sense of ply, meaning a fold or layer, was added. Plywood is made of layers glued together. To multiply is to make something manifold, literally. To replicate is to make one or more exact duplicates of something, possibly using multiplication.
Another way to say bend is flex. When you add re- to the latin flectere (to bend), you get reflex and reflect. Both mean bend back, but they have developed different senses. The sense of reflecting thoughtfully is from the 1640s, when it meant to turn back one's thought on a subject. Reflex gets its connotation of immediate, unthinking action from study of nerve stimulation in the 1800s. When light reflects off the surface of a mirror, we see a scene that appears to replicate our own surroundings.
You might wonder what pledge is doing in the word despondent. It’s from the Latin despondere, to promise to give something away, as in the phrase animam despondere (to give up one's soul). See Online Etymology Dictionary.