Many people have different opinions on what a proxy is:
HTTP Proxies (BurpSuite) or pivoting with a SOCKS/SSH Proxy (Chisel, ptunnel, sshuttle).Not all the above examples are correct. A proxy is when a device or service sits in the middle of a connection and acts as a mediator. The mediator is the critical piece of information because it means the device in the middle must be able to inspect the contents of the traffic. Without the ability to be a mediator, the device is technically a gateway, not a proxy.
Back to the above question, the average person has a mistaken idea of what a proxy is as they are most likely using a VPN to obfuscate their location, which technically is not a proxy. Most people think whenever an IP Address changes, it is a proxy, and in most cases, it's probably best not to correct them as it is a common and harmless misconception. Correcting them could lead to a more extended conversation that trails into tabs vs. spaces, emacs vs. vim, or finding out they are a nano user.
If you have trouble remembering this, proxies will almost always operate at Layer 7 of the OSI Model. There are many types of proxy services, but the key ones are:
Dedicated Proxy / Forward ProxyDedicated Proxy / Forward Proxy
Reverse ProxyTransparent Proxy