Post-modernity vs Post-modernism?

There are actually at least two closely related concepts: there is postmodernity, and also postmodernism. These take as their direct contrasts, respectively, modernity and modernism.

The adjective 'postmodern' is applied to anything in a culture which is evidence of that culture instantiating postmodernity. These things are, of course, also what the postmodernity of the culture consists of. Thus there is 'postmodern literature' and 'postmodern theory.' This last is what is called 'postmodernism,' because, being a theory, a postmodern theory is an -ism. There is also an alternate usage of 'modernism' and 'postmodernism', wherein a particular theory is a modernism or a postmodernism; so Kantianism might be a modernism, while Nietzsche's philosophy might be the first postmodernism.

Modernity and postmodernity are thought of as cultural conditions, and the marks of these cultural conditions are to be found in a culture's literature, journalism, law, science, humane studies, and so on. Modernism and postmodernism are thought of as kinds of theoretical approaches; specifically, the kind of theoretical approaches which try to understand modernity or postmodernity and which are themselves instances of modernity or postmodernity showing itself in the culture. Postmodernism is postmodernity showing itself in the humanities, just as modernism was modernity's version of humane studies.

Modernity is marked, by these postmodernists, by (at least) three features.

1) The desire to overcome prejudice and achieve objectivity.
2) The notion that progress was here to stay.
3) A set of distinctions which were supposed to make it so that we overcame prejudice and retained progress.

The first idea is best seen in Kant's 'What is Enlightenment?', which answers that Enlightenment is a critical mentality which persists in questioning dogma until it is either proved or gotten rid of. Objectivism, of course, is a modern philosophy (a modernism) by this criterion.

The second idea is best seen in Hegel and Marx. For both of these thinkers, there is an underlying force moving the world, and the direction it is taking us is good. This modern confidence in worldly progress was supposed to replace the pre-modern confidence in otherwordly salvation. Objectivism is not a modern philosophy by this criterion, because Objectivism's indeterminism allows that progress is not necessary but merely contingent (on human choice).

The third idea is also best seen in Kant. Fact-value, subject-object (i.e. self-world), mind-body, and so forth are all distinctions best formalized in Kant. These pairings have been the common currency of most modern schools of thought; that is, most modernisms have agreed to the common matrix of the Kantian distinctions (that's why they're modernisms). One semi-formal definition I've seen of postmodernism is that it is 'theory which breaks down the untenable dualities of modernism', with a litany of examples following. Objectivism is apparently postmodern (is a postmodernism) by this criterion. Actually, the first condition, but for its salience, should be seen as an instance of this third condition. Modernism dichotomized objectivity and prejudice, postmodernism rejects the dichotomy.

So postmodernism is a feature of postmodernity. Postmodernity takes modernity as its contrast object. The dimensions along which the two differ are their view of prejudice and objectivity, their optimism about progress, and their acceptance of the litany of modernist dichotomies stemming largely from Kant (and a few other places and phenomena). Their conceptual common denominator is that they are different (kinds of) cultures.