  Following numerous earlier studies, extensive simulations and analyses were
made on the continuous interaction distribution Gaussian model and the discrete
bimodal interaction distribution Ising Spin Glass (ISG) models in dimension two
(P.H. Lundow and I.A. Campbell, Phys. Rev. E {\bf 93}, 022119 (2016)). Here we
further analyse the bimodal and Gaussian data together with data on two other
continuous interaction distribution 2D ISG models, the uniform and the
Laplacian models, and three other discrete interaction distribution models, a
diluted bimodal model, an "anti-diluted" model, and a more exotic symmetric
Poisson model. Comparisons between the three continuous distribution models
show that not only do they share the same exponent $\eta \equiv 0$ but that to
within the present numerical precision they share the same critical exponent
$\nu$ also, and so lie in a single universality class. On the other hand the
critical exponents of the four discrete distribution models are not the same as
those of the continuous distributions, and differ from one discrete
distribution model to another. Discrete distribution ISG models in dimension
two have non-zero values of the critical exponent $\eta$; they do not lie in a
single universality class.
