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I think that when we refer to parallel spin, we refer to it as in different subshells (e.g. px, py, pz). I'm not sure if this would be different if the atom was at an excited state, but since we learned that no two electrons can have the same four quantum numbers in an atom, I would assume not.
Parallel shells are electrons with the same spin (up or down) in different orbitals but the same subshell. As a result, the only differing quantum number is ml. Electrons cannot have the same spin in the same orbital because that would give them identical quantum numbers.
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