Proxy is a middleman that passes your traffic between you and destination though itself. First proxies were used for caching and/or filtering files on the network, similar to what cloudflare/cdns do today, but in a more simple way, mostly at ISP or company network level. The side use for remote proxies was that you could route your traffic through third-party computer thus being anonymous for receiver. Proxies don't have or need transport encryption because they were never designed for it, so your ISP will see what hosts you connect to and what traffic you send.
Trivially speaking, a VPN is a virtual patch cord you put between two remote servers. The intended purpose of all VPN software was to build virtual local(private) networks. Example: remote employees connect to corporate network, remote servers connect to main server. This is where encryption is needed to acquire privacy of passing information.
A commercial VPN service, most people are thinking about when seeing word VPN is an entity that gives you a bunch or remote servers you could connect to over an encrypted channel via a VPN client for a fair price. It doesn't mean you'll be on the same local network with other users, well, ideally. Commercial VPNs had a boom in late 00's when users started understanding the fact any skid could hax their myspace passwords by sniffing plain http 95% of websites used back then, so a VPN would be a slightly better choice of browsing web on untrusted networks by offloading trust from non-existent wireless access point security to VPN provider's remote servers. Today we have fast Tor network and can be both anonymous and safe from local sniffers.
Side note on shadowsocks and why it is called so while being an tool for establishing an obfuscated encrypted channel to a remote server, and not a proxy on a remote server. It's just because it exposes a SOCKS port on one side for easy connection of machines and applications on LAN (when run on one of computers within local network, e.g. OpenWRT router) or localhost, same thing a tor daemon does.
Pardon mon Français and repetitive vocabulary clumsiness, English is my third language.