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Your confusion comes from a couple of sources. One is that quantum mechanics use a lot of classical terms that they know have a different meaning in QM. So don't let "orbital" fool you. They do not mean orbital as Newton used it, or even as in the Bohr model. The usage "orbital motion around the nucleus" just refers to the spatial wave function of the electron. "Orbital" does have another usage, that is a bit more quantum mechanical. The electron has two types of angular momentum. "Orbital angular momentum" is the quantum analogue of the classical angular momentum.

It is given by L=rXp, but r and p are now operators and the QM L is quite different from the classical L. In QM, the electron has another angular momentum called the "spin" angular momentum. Classically this would be thought of like the electron spinning as it went around the nucleus, much like the Earth spins on its axis as it goes about the Sun. But the electron is not spinning, and its spin is a purely quantum effect. The electron spin can be derived in relativistic QM (from the Dirac equation), but it also applies to non-relativistic QM like the hydrogen atom. The magnetic effects of the electron come from both its orbital and its spin angular momentum.

The use of the term "current loop" also is a QM use of the classical language, but with a somewhat different meaning. There is no current loop in electron orbital motion, but a lot of the equations look similar to those for a current loop.

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