What is the difference between enlightenment/awakening and nibbana/nirvana? And how do these terms relate to parinibbana/parinirvana?
Enlightenment, or Bodhi, refers to coming to a direct realization of the truth. Nibbana is the timeless state of perfect peace and happiness which occurs as a result of attaining Enlightenment, and it will occur immediately after attaining any of the four stages of enlightenment, and can be re-cultivated as well.
Parinibbana in common usage today refers to when a fully enlightened Arahat (one who has overcome all attachment and will not be reborn) undergoes bodily death. Instead of being reborn, they enter into Nibbana again, only this time they stay that way.
[A Mahayana perspective]
There are two components to Enlightenment: Realization (insight, awakening, Bodhi) and Liberation (unbinding, Nirvana, loss of form).
Very strong and talented people, with very few mental/emotional obscurations, determined on becoming Enlightened, and therefore diligently cleansing their minds from even slightest traces of unenlightened tendencies, attain both Bodhi and Nirvana at the same time. We call this "Sudden Enlightenment". Gautama Buddha and some famous Zen masters of the past belong to this category. When such person dies, we call it Parinirvana.
People of middling capacity(for enlightenment), with predominantly emotional obscurations, determined on unraveling the mystery of Enlightenment, and therefore diligently doing their own independent analysis, but slightly lazy about their practice, attain Realization first. Informed by the insight into the nature of phenomena, they continue working on their Liberation asymptotically, often for decades. We call this "Sudden Awakening / Gradual Cultivation". Most of the modern realized teachers belong to this category. When speaking of these we prefer to not use the honorary terms Enlightenment/Nirvana/Parinirvana.
Nirvana is a direct perception of emptiness and liberation from samsara. In the Mahayana tradition, a fully enlightened being such as Shakyamuni Buddha has gone beyond nirvana, removing all subtle obscurations, and has become omniscient. A more direct answer to your question is one difference between nirvana and enlightenment is omniscience.