HAProxy deserves a mention alongside those - it's particularly strong for high-traffic production environments where its advanced load balancing algorithms and detailed metrics shine.
It took me an embarrassingly long time to internalize what the reverse proxy is. My brain got stuck on the fact that it is just proxying requests. What's so reverse about this? Silly.
It's one of the classic cases of a thing being named relative to what came before it, rather than being named on its own merit. This makes sense to people working at the time the new thing is introduced, but is confusing to every other learner in the future.
Could be worse. All the many things named after people prevalent in some fields more than in others, biology/medicine for example. When you read, for example, "loop of Henle" or "circle of Willis" you don't even know where to begin. You either know the term or not.
How about service proxy vs web proxy rather than reverse proxy and proxy? Makes more clear that one is a proxy on the service side and the other is a proxy on the client side. Service proxy and Client proxy might be even better.