What a VPN does logically is turn your internet connection into a big Ethernet cable. When you are logged on to a company's VPN, the effect is similar as though you took your computer to the company's building and directly connected it. VPNs (usually) use encryption so that intermediate systems between you and the company (such as your ISP or a malicious wireless network sniffer) cannot eavesdrop your traffic.
Think of a proxy server as a filter. If all network traffic of a certain type, such as Web (HTTP) traffic, goes through a proxy, that proxy can manipulate that traffic on the way out and back on the way in. This has numerous uses ranging from ad-filtering, anonymizing, censorship, malware protection, and other things.
A proxy server modifies your traffic before it gets to the target. A VPN just wraps it up in encryption during shipping. Of course, for a VPN, the other end must be VPN aware and cooperate. This isn't necessary for a proxy.
That being said, you technically can have proxy servers that do nothing but encrypt traffic, and you probably can have VPNs that work like proxy servers and modify traffic. Both proxies and VPNs forward traffic on behalf of a client. Proxies generally work on specific types of application traffic. For example, there are HTTP proxies, DNS proxies, etc. Although there are SOCKS proxies that proxy everything... Some VPN software also can be configured to act as a virtual network adapter, so it's possible to move traffic through it that doesn't have to be proxy or VPN aware.