To answer quickly: yes, I think the object ("absolute space") is the same for both (in the Critique of pure reason, A39, Kant seems to almost explicitly criticise the Newtonian view, the view of "mathematical investigators of nature", and this is about "the absolute reality of space and time", the existence of which requires "two eternal and infinite self-subsisting non-entities (space and time)"). But this object, the absolute space, hasn't the same properties in the Newtonian view and in the Kantian one (Kant criticises the Newtonian view). According to Newton, absolute space has empirical reality, but according to Kant, it hasn't.
More details:
If I understood well your question, it seems that Kant gave an answer in the same book you quoted :
[...] a movable [empirical] space, if its motion is to be capable of being perceived, presupposes in turn an enlarged material space, in which it is movable; this latter presupposes in precisely the same way yet another; and so on to infinity.
Thus all motion that is an object of experience is merely relative; and the space in which it is perceived is a relative space, which itself moves in turn in an enlarged space [...]. Absolute space is thus in itself nothing [...] To make this [absolute space] into an actual thing is to transform the logical universality of any space with which I can compare any empirical space, as included therein, into a physical universality of actual extent, and to misunderstand reason in its idea.
(Kant Immanuel, Metaphysical Foundations of Natural Science, eng. M. Friedman, Cambridge University Press, 2004, « First Chapter: Metaphysical Foundations of Phoronomy », « Explanation 1 », « Remark 2 ».)
As I understand this excerpt, there is a difference between Newton's conception of space and time and the Kantian conception of it. The Newtonian one is absolute, and the Kantian one is relative: the absolute space is, according to Newton, real, but it is ideal according to Kant ("Absolute space is thus in itself nothing"). Newton gave the concept (not in the Kantian meaning of "concept" but more in the daily meaning of it) of absolute space an empirical or physical reality (this is why Kant wrote about the transformation of the "logical universality" of the absolute --- Newtonian --- space into an "empirical universality" --- transformation he disagrees with).
On the one hand, you have the empirical, physical, scientifical absolute space, whose substance would be aether, if I'm right (Newton); and on the other hand, you have the perceived space (Kant): for example, I see a book on my shelf, and I can move this book on my shelf: the perceived space filled by my book is relative to --- this means: can be moved compared to --- the perceived space filled by my shelf (and the perceived space filled by my shelf is relative to the perceived space filled by my wall, and so on: this is, if I understood well, the idea that Kant is presenting in the first sentence of the excerpt). This relative space is the only one that has empirical reality, according to Kant (and it is called "empirical space").
