  We prove the equivalence of two definitions of AF groupoid in the literature:
one by Renault and the other by Farsi, Kumjian, Pask and Sims. In both
definitions, an AF groupoid is an increasing union of more basic groupoids,
called elementary groupoids. Surprisingly, the two definitions of elementary
groupoid are not equivalent; they coincide if and only if the local
homeomorphism that characterises them is a covering map.
