Papyrus leaves, vellum and paper each have complicated and not at all intuitive ways of being made. In the case of papyrus, we may not fully know how it was produced in antiquity. These are some interesting videos on the production of each material.

Papyrus: https://www.youtube.com/watch?v=DCR8n7qS43w

Vellum or Parchment: https://www.youtube.com/watch?v=2-SpLPFaRd0

Pre-19th century/wood pulp paper: https://www.youtube.com/watch?v=e-PmfdV_cZU