It's far simpler than this. If you get the basics of http, the only thing you need to know is what is the 'proxy' a proxy (stand-in) for? the client (forward) or server (reverse).
If people used the names client proxy and server proxy it would be much clearer. Calling one forward and one reverse means you have to know the order of popularity of usage which is dumb thing to settle on.
This is a common mnemonic, but it also has a common flaw, which is easily reached by application of a modicum of overthought: Both proxies always act as both servers and clients; just to different sides, one in the direction of requests (forward), another against (reverse).
At least that's where I end up every time I have to remind myself which is which.
I find the "reverse" naming so confusing. To me it makes it sound like the http request goes backwards or something like that which makes no sense. What you suggest should be the way to word it.
If people used the names client proxy and server proxy it would be much clearer. Calling one forward and one reverse means you have to know the order of popularity of usage which is dumb thing to settle on.