There are many diagrams and word salads presented in cause of explaining forward and reverse (backward? I like linguistic symmetries) proxies. Munificent logic and inholistic reason thus spewed confounded me in my simple desire to know. Fortunately for you, in a dream I had last night I explained it to a dream person thus, and when I had spoken it I knew it was the reductive idea purged of all contrarian confounding encumberment; clairvoyance having carried it forward until now. There is no need to fret about the client or server not know about the presence of the proxy in either case.
In a forward proxy, the server communicates with the proxy as a client. In a reverse proxy, the client communicates with the proxy as a server.