Are there some similarities between J-coupling and j,j-coupling?
I don't believe there are any commonalities, and the terms have been derived independently.

The term J coupling in NMR was first proposed in 1951 by Erwin Hahn in his paper  describing the spin echo experiment, in which two frequencies are observed; one at the chemical shift (which they called delta, as was convention, even back then) as expected, and a second frequency which they labelled as frequency J. There is no explanation for why the choice of J is given. Gutowsky and McCall  who observed the same phenomenon independently did not give it a label, and the term J splitting stuck. J coupling describes the relationship between nuclear spin, the intrinsic angular momentum of atomic nuclei.

The term jj coupling relates orbital angular momentum of electrons. I'm not going to pretend to know anything about the origins of the term, nor anything about its application in physics and astronomy. However, the term J is sometimes used to represent total angular momentum, which is made up of individual components ji. It is the interaction between these individual j terms that give rise to jj coupling.

Other than being types of interactions between entities of angular momentum, the two couplings are quite unrelated, as are the terms used to describe them.