A Proxy Server acts as an intermediary between your device and the rest of the internet. When you use a proxy, your web requests travel to the proxy first; the proxy then talks to the website on your behalf and sends the information back to you.
This is the most common question in networking. While they both hide your IP, they do it differently:
Usually works at the Application Level. For example, you can set your web browser to use a proxy, but your Spotify app or system updates will still use your real IP. Most proxies do not encrypt your traffic.
Works at the Operating System Level. It creates an encrypted tunnel for 100% of your device's traffic. It is generally more secure but can be more resource-heavy.
Sometimes you are using a proxy without even knowing it. Many schools and offices use Transparent Proxies to filter content or cache frequently visited sites to save bandwidth. Because the proxy intercepts your request automatically, you don't have to configure any settings on your computer.
Behind the Scenes: When you use a proxy, you are trusting the proxy owner with your data. Since the proxy "unpacks" your request to forward it, an untrusted free proxy could potentially log your activity. Always use reputable providers.