The general rule is as follows. A model A is nested within a model B if model A is a special case of model B obtained by constraining model B parameters (e.g. fixing them to zero, or holding them equal). For chi-square difference testing of model A versus model B to be correct, the constraining of parameters must not be such that a parameter ends up on the border of its admissible space, such as a variance fixed at zero.
Because of this, model A is nested within model B, but you can't do chi-square difference testing because the constraints on the model B parameters are that not only the mean but also the variance of s2 is fixed at zero.