I'll join the discussion even though my native language is German and I therefore might see some words in a slightly different context. There was the suggestion to use piece instead of model to describe the finished Origami work. I have to say, that I feel highly uncomfortable about that and here's why. For me piece is another word for part like for example piece of cake, piece of paper. On its own it isn't complete. Whereas a finished Origami model is complete on its own. The analogy of using model on the other hand is very logic to me, as most Origami models try to somehow mimic something else just like model making models do. Of course there are some exceptions like for example tessellations that do not necessarily have to have an archetype in nature, but most Origami models do resemble something that already exists like for example animals. And yes, I do think that a model can be art but here's another thing that I feel is important. Not every finished Origami work is art. When I fold, only a small part of the things I fold is supposed to be for display. The majority of things I fold, I just fold to entertain myself and there are many people who would never claim their folds to be art, because that's simply not what they intend. But the question is where is the crossing line? At what point does Origami become art? And do we have to name it differently as soon as a model crosses the line? Fact is that many children learn a few simple folds in kindergarten and that those folds surely aren't art and that what many of us do differs a lot from this children play. I know how frustrating it is when you just finished a super complex model that needed several hours to complete and someone comes along to tell you that his little child would surely like that and whether you could maybe show it how to do that (Appreciation zero).
Anna