Both VPNs and proxies route your traffic through another server so websites see a different IP. The key differences: a VPN encrypts the whole tunnel and typically handles all traffic, while a proxy usually forwards one protocol without encryption.
Use a VPN when you need encryption and privacy (public Wi-Fi, sensitive work). Use a proxy for simple tasks like bypassing a regional block for a browser request, and never send sensitive data through an unencrypted proxy.