In his article

Gromov, M. Almost flat manifolds. J. Differential Geom. 13 (1978), no. 2, 231–241

Gromov exploited a notion of a pseudogroup. In his book

Tao, Terence. Hilbert's fifth problem and related topics. Graduate Studies in Mathematics, 153. American Mathematical Society, Providence, RI, 2014

Tao systematically developed the notion of an approximate group and gave several applications.

What is the precise relationship between the notion of pseudogroup and that of an approximate group?