The Royal Crest, seen on British passports, features a lion and a unicorn, two animals not exactly seen often in the United Kingdom. Why?

The lion on the royal crest symbolizes england, and the unicorn scotland.
The lion makes reference to the "three passant guardians", that are used in the English coat of arms since Richard the lionheart.
The unicorn is used in the Scottish coat of arms.
The lion is crowned, and the unicorn is chained (unicorns were originally considered to be dangerous beasts).
https://en.wikipedia.org/wiki/Royal_coat_of_arms_of_the_United_Kingdom

Thank you - I've always wondered. But why is the unicorn considered Scottish? Is the unicorn part of Scottish folklore - is that where they are from?