In line with the latter tendency in Mill's thought is the way Rawls distinguishes between two kinds of liberalism. The "liberalism of freedom" is contrasted in his Lectures on the History of Moral Philosophy with the "liberalism of happiness". The latter clearly relates to the classic utilitarian tradition from which Rawls exempts Mill when considering Mill as a political thinker, as in the latter's essay on liberty. In the essay on liberty it becomes clear that Mill takes liberty to be a cardinal political value, and, in so doing, he distinguishes himself from those who view political life primarily through the lenses of welfare. Since Kant was vociferous in rejecting welfare as a general end of politics it is just as clear that Kant opposes the "liberalism of happiness". The notion of the liberalism of happiness would be one that centrally promoted conditions of material well-being and in some contemporary discussions of the need for economists to take happiness to be a central variable we are witnessing the latest stage of the influence of utilitarianism on economics.
By contrast to this emphasis on happiness a liberalism of freedom endorses a form of pluralism concerning the good. This is explicit in Mill's defence of liberty but is also there in Rawls' many arguments against "comprehensive" moral views that assume agreement in a way that is broader than is reasonable. The Kantian conception of the social contract is explicitly endorsed by Rawls as an alternative to atomistic views of society (as formulated by methodological individualists such as Nozick) on the one hand and to state-centred conceptions on the other precisely due to the connection it suggests between reason and law.
However, where Rawls' position tends towards that of Mill and away from that of Kant is precisely in Rawls' greater willingness to endorse socialistic ends, in, that is, his deeper egalitarianism, something shared more with Mill than Kant. The split within liberal politics has tended to follow this pattern between those of a more social tendency who are attracted to egalitarian ends and those who emphasise freedom. The former push liberalism in the direction of social democracy whilst the latter, by contrast, have to articulate a defence of the state against libertarian temptations. Kant's own classic position is definitely of the latter sort in his own writings though whether this best reflects the internal tendencies of his own thought is another matter. To assess the relationship of Kant to liberalism and particularly to the more egalitarian tendencies of today's "Kantian liberals" is an endeavour that will require more work.
What I am suggesting, at least initially, is that there appears to be an important divergence within the camp of "liberalisms of freedom" between those that allow serious space for egalitarian considerations and those who are wary of so doing. Rawls' distinction, in his late work, Justice As Fairness: A Restatement, between "welfare state capitalism" and a "property owning democracy" is meant to indicate a way in which his egalitarian commitments are still distinct from those of a "liberalism of happiness" where this latter notion is associated with the welfare state. The point here is meant to be that the welfare state works primarily as ameliorative of misery and allows stark inequality in its aggregative sense of the greater good. By contrast, Rawls' own "property owning democracy" is meant to create a "fair system of cooperation" including by means of redistributing capital. This entails a radical edge to Rawls' position though, in so doing, it also threatens to undermine the lexical priority of the principle of liberty over the double-edged egalitarian second principle. Kant would appear less susceptible to this temptation and this might suggest either that the conception of Kant as a liberal is problematic in itself or, if Kant is a liberal, then his "liberalism of freedom" might yet turn out to be very different from that of Rawls.