Are all attributes identical in God? Do the distinctions in his attributes come from our way of understanding him?
The answer to your first question is yes. Because of God’s absolute simplicity (the fact that there are no parts within him, either physical or metaphysical), all of God’s attributes are one with his essence, which is existence itself. God is his eternity, which is his power, which is his will, which is his intelligence, and so on. Talking about God’s different attributes are just different ways of talking about the one and same reality. Although we distinguish his attributes in thought, they are not distinct in reality.
This doesn’t mean, however, that all his attributes mean the same thing. Just as the expressions “the morning star” and “the evening star” differ in sense while referring to the one and same thing, so to “intellect,” “will,” “goodness,” “power,” etc., differ in sense while referring to one and the same thing when applied to God.
It’s also important to keep in mind that when we predicate these attributes to God, we do so analogically. And this gets to your second question.
When we name God with positive attributes, such as goodness, power, and intellect, we take these names from creatures. But we don’t apply them to God in the same way (univocal predication). Nor do we apply them in an entirely different way (equivocal predication). When we apply them, we recognize that there is similarity, but at the same time, there is also a difference (analogical predication).
As philosopher Edward Feser puts it, “There is in God something that is analogous to power, something analogous to goodness, something analogous to intellect, and so on, and that these 'somethings' all turn out to be one and the same thing” (Aquinas: A Beginner’s Guide, ch. 3).