There exist many defintions of NMI and AMI.

Vinh, N. X., Epps, J., & Bailey, J. (2010). Information theoretic measures for clusterings comparison: Variants, properties, normalization and correction for chance. Journal of Machine Learning Research, 11(Oct), 2837-2854.

mention 5 different definitions of NMI, and based on that give 4 different AMI.

The NMI implemented in sklearn uses sqrt(H(U), H(V)) for normalization.
The AMI implemented in sklearn uses max(H(U), H(V)) for normalization.

There exists an NMI with the max normalization, and a AMI with the sqrt normalization, so this is inconsistent in sklearn. Ideally, they would both use the same definition by default, and allow using any of the others via an option.