Unlike common understanding who treat origami as just folding paper into objects. The true traditional art is to fold with not just any shape of paper, but only from a perfect square. A piece of uncut perfect square to be exact.
This alone has already created thousands of models. It ranged from simple models where young children are being amused by their imagination on the premitive but yet symbolic folded features to capture the spirit of the folded object, to the most complex models where fine details are being folded to the level not less intricate than the chiselled sculpture. Yet all are done with the same uncut perfect square paper. — To practice Complex Origami, one need to have good folding skills and special paper.
When the complex models has reached new heights, there is another school of origami growing in strength — they are the Modular Origami. This type of origami focus on folding simple units, more like the extended LEGO bricks set, and then carefully assembled them into the target object, which are mostly resemble the molecular or lattice structure found in Mathematics or Chemistry textbook. For this type of origami, they need not follow the rule of folding the units with square paper. — To practice this type of origami, one need to have basic folding skills and moderate assembly skills. The paper used are mostly stiffer paper for holding up the structure.
To create even more complex models, the modular origami has evolved to one which is to fold a very simple basic unit (most of the time is just a triangular pocketed wedge) in count of thousands, then carefully interlock them together to form the object. — The folding accounts for very little percentage for this type of models. The main focus is on the model assembly which sometimes requires the use of bonding material. I call them ‘Origami Unit Synthesis‘. You can use practically any type of paper for this type of models.
So next time when you chanced on a paper folded models, see which type it belongs to.