Well, there's pure theoretical reason, pure practical reason, and even pure judgment, but it sounds like this is not the thrust of your question.
I definitely disagree with the commenter you cited who claimed that God and human beings have the same faculties of reason. Possibly the single most important distinction for Kant is the distinction between intuitus originarius and intuitus derivativus. Only God has an intuitus originarius, a faculty of intuition which is capable of generating the object it intuits. The human being is a fundamentally finite creature and thus has a passive intuition. The object we intuit must already exist, by virtue of some power beyond us (as a thing-in-itself) in order for us to be able to receive or intuit it. Kant calls God’s faculty an intellectual intuition, because like our intellect it is spontaneous and discursive. We are capable of taking two concepts and combining them in thought spontaneously, but not so in intuition (keeping in mind that imagination is a separate faculty).
As I said, this distinction underlies everything essential to Kantian thought. Because of the finitude of our faculties, we are incapable of immediate intuition of the thing-in-itself. Thus all the questions posed by metaphysics cannot be answered by our pure theoretical reason, and rather represent the confusions of a finite mind grappling with the idea of infinity. The impossibility of answering these basic metaphysical questions, including the question of the existence of God, is the theme of the Critique of Pure Reason. Because our reason does have immediate access to the moral law, and is capable of spontaneously affecting itself in this domain, practical reason is our only access to ourselves as a thing-in-itself, which forms the theme of the second critique.
This point is also essential to the distinction between Kantian thought and the German Idealism of Fichte, Schelling, and Hegel. Fichte says that every self-consciousness is infinite and an intellectual intuition by virtue of the fact that the ‘I think’ creates itself by thinking of itself. Thus, like God, we create our own self-consciousness by thinking of it. This infinitude is the fundamental break with Kant, though these thinkers claim to be carrying on aspects of his work.
Here is a relevant quotation from the first critique:
It is, moreover, not necessary that we should limit the mode of intuition in space and time to the sensuous faculty of man. It may well be that all finite thinking beings must necessarily in this respect agree with man (though as to this we cannot decide), but sensibility does not on account of this universality cease to be sensibility, for this very reason, that it is deduced (intuitus derivativus), and not an original (intuitus originarius), consequently not an intellectual intuition, and this intuition, as such, for reasons above mentioned, seems to belong solely to the Supreme Being, but never to a being dependent, quoad its existence, as well as its intuition (which its existence determines and limits relatively to given objects). This latter remark, however, must be taken only as an illustration, and not as any proof of the truth of our aesthetical theory.
Kant, Critique of Pure Reason, First Part: Transcendental Aesthetic Section II SS 9
With regard to angels, I don't believe that Kant thinks any beings other than God could have an intuitus originarius, but there are still some interesting differences between their faculties and human faculties. Kant views all rational beings as possessing absolute moral principles. However, human beings often stray from what is right because they also have a faculty in conflict with practical reason, their sensuous appetites. Kant thinks that angels would never err from God's will or from practical reason, because they do not have the appetites to lead them astray. They need not eat and so feel no hunger; they are eternal and so have no need for sexual reproduction.
He does not envy them, nonetheless. The conflict human beings face between appetite and practical reason is what ultimately makes us free agents. Angels, because they cannot err, have deterministic behavior. The possibility for error that is the constant struggle of the ethical life justifies for Kant heaven and its reward of eternal happiness.