  In this expository article, we compare Malle's conjecture on counting number
fields of bounded discriminant with recent conjectures of
Ellenberg--Satriano--Zureick-Brown and Darda--Yasuda on counting points of
bounded height on classifying stacks. We illustrate the comparisons via the
classifying stacks $B(\mathbb{Z}/n\mathbb{Z})$ and $B{\mu_n}$.
