The distinction is more vague than exact, and there are philosophers who aim at axiomatic systems (e.g. Spinoza and I think maybe Chalmers? Or Nicholas Rescher at times, iirc, etc.), and Godel's ontological argument is actually looked upon with some favor...
... but ultimately, the difference is external. You can say that the concepts of substance and causation and so on have a definition or demarcation, you can stipulate aspects of word usage in relation thereto, but these approaches advert to the strength of conceptual analysis to be persuasive. So too, Godel argued for "the iterative conception of sets" and thought set theory might be analytically true of this concept. But for many of us, accepting various set/category-theoretic statements can be hypothetically rendered, as in, "If there are infinite sets," or, "If something 'falls into' a category," and this is persuasive enough, as if we (to bring up Conifold's point about game-like formality) played a game of chess and identified the winner according to the rules, only here "winning" is "proving a statement relative to the premises."
By contrast, if we just analyzed arbitrary notions of substance, we might be engaged in deep and elaborate world-building (e.g. there is an author who made up a world where substance is not matter/energy but matter/energy/"investiture", with corollary alternations on thermodynamic conversion) but how rationally persuasive is this when it comes to judging whether there really are substances of a given kind in our world?
Now there was a very influential ethics philosopher who said we should aim for an image of ethics akin to "moral geometry" (Rawls, AToJ), but he did not think he had achieved this goal in his own work and emphasized a method quite unlike a stereotypical axiomatic one, in context.
So we would say: there's nothing wrong with "axiomatizing philosophy" except that no such attempt has ever proven very persuasive beyond hypothetical presumption. Supposing that metaphysical and ethical truths are fundamental and accessible seems to testify against the idea that it should take eons to arrive at such persuasion. Now you might think that such conviction is not attained owing to stubborn/irrational reactions, so that "if people were more honest with themselves in general" they would accept "obvious" axioms; but in philosophy, we focus on the freedom of questions instead of the stricture of deduction (which in context often mutates into ideological certainty, or as Hannah Arendt says, the ideologist is so beholden to "logic" and "inferring one thing from another and another" down through the "whole murderous alphabet" (TOoT, not an exact quote). By the principle of charity (which to be fair looks like an axiom after a fashion!), we try to believe that disagreement is not usually in bad faith; so we try to avoid claiming that our axioms are obvious (indeed, why else would Kant develop the method of transcendental argument do acutely?).