ELI5 Induction Stoves - are they really faster than gas stoves?

Are induction stoves quicker than gas stoves? How does using an induction stove compare to using gas or conventional electric stoves? What is the secret behind how induction stoves can boil water so quickly? Can you explain how induction cooktops heat pans without heating themselves? Do induction stoves require specific cookware for efficient cooking?

... we explain like I'm five

Thank you to the r/explainlikeimfive community and in particular the following users whose questions and comments formed the basis of this discussion: king_hubba_, zackofalltrades198, philosopherspants, greatspacegibbon, lanzr, bardfinn, clap4lights, and vadered. 

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