Arts and crafts describes a wide variety of activities involving making things with one's own hands. Arts and crafts is usually a hobby. Some crafts (art skills) have been practised for centuries, others are more recent inventions.
As a child I loved creating things and modeling with paper and card. I thoroughly enjoyed cut-outs and making pop-up cards and while I never studied origami, I would often take a piece of paper and try to fashion it into a recognizable object. Taking a piece of paper and folding, cutting, rolling, gluing, tearing and embossing it until it becomes so much more than just a flat, formless sheet of paper is not only creatively satisfying, but also very relaxing.
I never considered it an art form and without the exposure to the vast array of paper art being created, what I did was nothing more than just a way to pass time. I recently discovered some incredible paper art and artists and, I think you will agree, their work is spectacular and most certainly takes paper art way beyond origami.