I came across this article by Jack Kornfield in which he says that it is better to talk about enlightenments, since there are different versions of it. (So, this is not about different levels of enlightenment, but different enlightenments.)
Of course, I can imagine that Mahayana teaches something different than Theravada or other traditions and vice versa, but this article refers also to different types of enlightenment within Theravada.
Added by request:
enlightenment as a shift in identity;
liberation from greed, hatred and delusion;
devotion and surrender, being carried by the Buddha’s “grace";
When you actually experience consciousness free of identification with changing conditions, liberated from greed and hate, you find it multifaceted, like a mandala or a jewel, a crystal with many sides. Through one facet, the enlightened heart shines as luminous clarity, through another as perfect peace, through another as boundless compassion. Consciousness is timeless, ever-present, completely empty and full of all things. But when a teacher or tradition emphasizes only one of these qualities over the others, it is easy to be confused, as if true enlightenment can be tasted in only one way. Like the particle-and-wave nature of light, enlightenment consciousness is experienced in a myriad of beautiful ways.
He also describes different gates through which one can get enlightened: The gate of impermanence, suffering, no-self. So far there is no surprise. He then mentions more gates:
There are many other gates: the gates of compassion, of purity, of surrender, of love. There is also what is called the “gateless gate.”
The way enlightenment expresses is also different according to JK:
This is enlightenment as love.
This is enlightenment as emptiness.
He expresses enlightenment as fullness.
Enlightenment as mindfulness.
The Dalai Lama personifies enlightenment as compassionate blessing.
He expressed enlightenment as wisdom.
(I would suggest to read the article.) Naturally, I'm a bit puzzled now.
Do suttas also talk about different types?