  We consider two integrable deformations of 2d sigma models on supercosets
associated with AdS_n x S^n. The first, the "eta-deformation" (based on the
Yang-Baxter sigma model), is a one-parameter generalization of the standard
superstring action on AdS_n x S^n, while the second, the "lambda-deformation"
(based on the deformed gauged WZW model), is a generalization of the
non-abelian T-dual of the AdS_n x S^n superstring. We show that the
eta-deformed model may be obtained from the lambda-deformed one by a special
scaling limit and analytic continuation in coordinates combined with a
particular identification of the parameters of the two models. The relation
between the couplings and deformation parameters is consistent with the
interpretation of the first model as a real quantum deformation and the second
as a root of unity quantum deformation. For the AdS_2 x S^2 case we then
explore the effect of this limit on the supergravity background associated to
the lambda-deformed model. We also suggest that the two models may form a dual
Poisson-Lie pair and provide direct evidence for this in the case of the
integrable deformations of the coset associated with S^2.
