What is the difference between A => 1 and 'A' => 1?

Using the Perl 6 REPL:

> Map.new: 'A' => 1, 'B' => 2;
Map.new((:A(1),:B(2)))
> Map.new: A => 1, B =>2;
Map.new(())

I previously thought that A => 1 and 'A' => 1 would be identical because => is supposed to autoquote the word to its left, but in the second example the pairs seem to disappear.

Disclaimer: This tripped me up earlier today, so I'm posting it as Q&A in case it is helpful to someone else too. Also feel free to add your own answers.