Here is an image explaining my current understanding of the relationships between a number of important elements in the Aristotelian-thomistic understanding of the sciences and how human beings come to knowledge of different beings.
Both types of abstraction (of the whole and of the part) are happening in the first act of the intellect (and both seem to be related to the first degree of Abstraction, but, the first is only in relation to the philosophy of nature: cf. Jacques Maritain's "Philosophy of Nature"; and the second is only in relation to the natural sciences). The second type of Abstraction is going on in all 3 degrees of Abstraction: from individual sensible matter, from common sensible matter and from intelligible matter. So, in the 3-fold division of the sciences, technically, only the second type of abstraction is happening (except in the case of the philosophy of nature which seems to be primarily the first type of Abstraction).
There is no abstraction in either judgment or reasoning. Therefore both types of abstraction are happening in the act of simple apprehension. The type of abstraction that goes on in simple apprehension will depend on the degree of abstraction that is being considered in the domain of science that is in question (in other words, on being-as-X).
George Van Riet also discusses (in his article "La théorie thomiste de l'abstraction," in Revue Philosophique de Louvaine, 3ieme série, tome 50, no. 27 (1952), 353-393.) what he calls the abstraction of Being, which would be, supposedly, a third type of abstraction. I'm still working on figuring out what he means by that, and what to do with this idea.