Quaeritur: What is the difference between so-called ‘total abstraction’ and ‘formal abstraction? If total abstraction consists in abstracting the universal from the particular (e.g., abstracting from a concrete man the universal ‘man’), and formal abstraction consists in abstracting the form from the matter-form composite (e.g., I suppose that from a concrete man, we could abstract his formal ontological structure, that is, his substantial form ‘man’), which places a given being in its species, and which would be similar to the universal---or am I mistaken? Aren’t they ultimately the same thing?
Respondeo: The difference between these lies in that total abstraction consists, as you say, in abstracting the complete nature of the individual in question (e.g., if we look at a particular tree and abstract the nature of ‘treeness’, or the tree’s proximate genus ‘plant’, or its ultimate genus ‘substance’), whereas formal abstraction consists in isolating, not the whole nature, but merely some partial aspect of the individual, prescinding from its sensible qualities that depend on matter for their definition (as for example, taking the same tree, we can abstractly conceive its geometric shape or figure). These two types of abstraction, according to modern scholasticism, correspond to natural science and to mathematics, respectively.
Here is a nice explanation from Klubertanz’s Introduction to the Philosophy of Being (2nd Ed.):