Generally, artwork involving cut paper or gluing and are not considered origami, but cutting is allowed in the related art of Origamic Architecture.
Also, while most origami is created from a single piece of paper, Modular Origami is based on using many folded units fit together, and can be placed in that category.
Other kinds of paper models, such as those cut from a sheet with flaps that are taped, glued, or with notches that fit together do not belong in Origami.
The same goes for models assembled from cards printed with various designs.
Most of these should fit somewhere in:
https://curlie.org/Recreation/Models/