* Hyphens connect things, such as compound words: double-decker, cut-and-dried, 212-555-5555.
* EN dashes make a range between things: Boston–San Francisco flight, 10–20 years: both connect not only the endpoints, but define that all the space between is included. (Compare the last usage with the phone number example under Hyphens.)
* EM dashes break things, such as sentences or thoughts: 'What the—!'; A paragraph should express one idea—but rules are made to be broken.
Unicode has the original ASCII hyphen-minus (U+002d), as well as a dedicated hyphen (U+2010), other functional hyphens such as soft and non-breaking hyphens, and a dedicated minus sign (U+2212), and some variations of minus such as subscript, superscript, etc.
There's also the figure dash "‒" (U+2012), essentally a hyphen-minus that's the same width as numbers and used aesthetically for typsetting, afaik. And don't overlook two-em-dashes "⸺" and three-em-dashes "⸻" and horizontal bars "―", the latter used like quotation marks!