Quick answer: A VPN usually routes your traffic through a VPN server, a proxy commonly relays traffic for a particular application or protocol, and Tor sends traffic through a distributed relay network.
What websites can see
When traffic is routed through an intermediary, a website may see the intermediary’s public IP rather than the direct address of your connection. The exact behavior depends on the application and configuration.
How to test what is visible
Run VPN / Proxy Check and compare the result with a normal connection. Remember that changing the visible IP does not automatically make every aspect of a browser session anonymous.
Want to see this in practice? Check your own connection's IP, location and ISP.
Check my IP address