At assemblies I've been to--anarchist ones, not Occupy--there is a space for the sharing of practical information (such as who has access to what resources); a space for open discussion (with a focus on analysis of social tensions or social movements and what to do or not do); a space for proposals (brought for debate and to test their strength and magnetism but not put through any formal decision-making process); and a space for people to break up and more concretely work on the proposals they like.
There has been no decision making at these assemblies, nor any voting, nor any democracy, nor any real reliance on the affinity group model.
I have attended meetings that functioned more like what you describe, with decision-making and a heavy recourse to the affinity group. But they were always called spokescouncils or consultas or convergences or something. This could be called the network model, or the anti-globalization era model.
I think the term assembly was popularized in place of those to create an informal setting more consistent with a distaste for formal groups and collective decision making. Of course now most people when they hear assembly think of the (Occupy) General Assembly, which is more like the anti-glob spokescouncil than the assemblies I described.
