Both of these technologies will protect your privacy by hiding your IP address, however they work in slightly different ways.
A proxy server acts as a gateway to your software. For example, your Internet Provider is a gateway to the internet. The same idea applies to proxies. The biggest difference between a proxy and a VPN is proxies (aside from SSH proxies) are not encrypted.
An anonymous VPN will protect and encrypt your entire internet connection, by re-routing all of your traffic through our secure network. Unlike a proxy, which only secures your torrent client or web browser, a VPN (Virtual Private Network) secures 100% of your internet access.
With a fully anonymous VPN server, you can enjoy enhanced privacy and security regardless of geographic location.
This protects all of the software on your device, such as games, web browsers, e-mail, and any other third-party applications that connect to the web.