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An ordered permutation group is order n-transitive if it can send any increasing $n$-tuple to any other increasing $n$-tuple. This compares tuples with the same relative order, unlike unrestricted n-transitive group actions. In the usual transitive chain setting, order two-transitivity implies every finite order-transitivity for a lattice-ordered permutation group.

A group action on a set is two-transitive when it acts transitively on ordered pairs of distinct points. Equivalently, a point stabilizer acts transitively on the remaining points.

This is the $k=2$ case of a multiply transitive group action.