What are the differences between Kant's Categories and Aristotle's?
1 Aristotle's categories are the basic kinds or classes of being (kategoririai tou ontos : 'Categories', IV)), Kant's of thought or 'phenomena' in his sense of the term. For Kant they are the fundamental concepts of the understanding (Stammregister des Verstandes : 'Critique of Pure Reason', Transcendental Analytic, B107 : 'the true ancestral concepts of pure understanding', Guyer & Wood, 213).
2 Aristotle's categories are intended to constitute the ten highest genera of entities. Kant has twelve categories and they relate to the twelve ways in which judgements are classified.
3 Kant 'deduces' his categories, i.e. he gives an explanation of how categories, which look like empty forms, can combine with sense perceptions to produce experience. This requires the work of imagination and the forms of sensibility (space and time). Aristotle has no comparable task; objects can be subsumed under categories without need of any special explanation of how this is possible. I see two objects and recognise that the category of quantity applies.
4 Aristotle's prime categeory is substance. Kant also uses the category of substance, but differently. Aristotle's concept of substance is not entirely clear but it can reasonably be taken that for Aristotle a substance is centrally a concrete individual thing persisting through time and possessing a kind of independence : a quality, for instance, needs a substance to exist in or be predicated of. A substance does not in the same sense exist in anything else and is not predicable of other things. Brownness is a quality of a dog and 'brown' can be predicated of a dog but a dog is not a quality of anything else and cannot be predicated of anything else. Kant demotes the category of substance in the sense that, for him, substances are not the fundamental entities of the world; they are simply, as perceived continuants, one of the ways in which we classify our experience.