The moduli space of non-isotrivial elliptic K3 surfaces admits several stratifications. Here we consider two of them. The first is the monodromy stratification introduced by Bogomolov, Petrov and Tschinkel and the second is the Shimada stratification obtained by fixing the root lattice of the trivial Neron–Severi group. Neither of these stratifications is a refinement of the other. There are, however, a number of strata which are common to both stratifications. Here we classify these so called ambi-typical strata, of which there are 50. This is joint work with Michael Lönne.