Differences in the context of English:
The plugin corresponds to "Plugin", the extension corresponds to "Extension", so there are actually two different words behind them.
At the functional level difference:
Plug-ins do not increase the functionality of the browser itself, can invoke the operating system's APIs, and different operating system plug-ins are generally not mixed. We often encounter Plug-ins are: Flash plug-ins, PDF plug-ins, Java plug-ins and so on.
In contrast, extensions can increase the functionality of the browser itself, or call the browser's API, and the same browser extensions are generally available across the operating system. For example, the Chrome extensions you use in Windows can be used on the MAC platform as well.
Differences in security
Because the plug-in is generally implemented are relatively low-level functions, so once the problem, often will involve the entire operating system, such as Flash Plug-ins are often pulled out of high-risk vulnerabilities of that category.
Compared with the problem of extension, the Harmfulness class is often like the browser loophole. But while the chrome Extension is bringing convenience to users, it does pose a lot of security problems, and Google Chrome's stable version even bans Windows users from installing the extensions outside the Chrome Web Store. Even apps in the Chrome Web Store do not guarantee absolute security, as Google itself has been able to rack up some security-risk extensions.
Well, after reading these differences, there is no sense of the difference between plug-ins and extensions is quite large, the next time you meet someone confused these two concepts may wish to correct.