A Plugin is a tiny program that works hand by hand with your WordPress installation by adding more features and functionality.
I like to think of them as little modular accessories that you add seamlessly to your website, adding desired features without getting in the way of the main WordPress installation. There is a plugin for almost anything you desire your website to have, which is amazing, but some of them haven’t been updated in years and can break your website, so its always good to read the reviews of a plugin, when it was last updated and if it supports the WordPress version your website is using.
Widgets are small modules where you can drag and drop content and plugins to. The default installation of WordPress comes with basic plugins for areas like sidebars and footers, but depending on the theme you choose you might be able to customize more areas on your website.
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PS: Are you part of Happy Hour Web Craft already? This is going to be a fun Fall to learn more about WordPress customs sites and getting crafty with design and code.