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?