To simplify the two: 1.Blogger widget - Ready made, all you have to do is select those ready built-in and you are good to go. 2.WordPress plugins - You can customize anything you like especially many developers create tons of plugins for achieving certain objective. E.g, all in one SEO, Sitemap generator, easy privacy policy, content curation, Rss submission, auto blog software and so forth. Hope this simple info could enlightening you a little.
The difference is that they aren't even close to the same thing. It's like saying what's the difference between a camera and fonts.
widgets are mostly related to placement of certain readymade options in the website sidebar or footer like calendars, optin forms, fb updates, recent post, even adsplugins are for a much wider use such as for performing task (seo, security, design, etc.) adding extra options and even adding widgets.