  In this work, we have illustrated the difference between both Tsallis and
Kaniadakis entropies through cosmological models obtained from the formalism
proposed by Padmanabhan, which is called holographic equipartition law.
Similarly to the formalism proposed by Komatsu, we have obtained an extra
driving constant term in the Friedmann equation if we deform the Tsallis
entropy by Kaniadakis' formalism. We have considered initially Tsallis entropy
as the Black Hole (BH) area entropy. This constant term may lead the universe
to be in an accelerated mode. On the other hand, if we start with the
Kaniadakis entropy as the BH area entropy and then by modifying the Kappa
expression by Tsallis' formalism, the same constant, which shows that the
universe have an acceleration is obtained. In an opposite limit, no driving
inflation term of the early universe was derived from both deformations.
