When it comes to textile, cellulose fibre were made from cellulose that extracted from trees, after that processed with chemical until it get dense and contains more that 90% or cellulose. Cellulose fibre was not included into natural or synthetic because the base material were come from nature but it processed by some chemical reaction, so it categorized into semi-synthetic or artificial fibre. Semi-synthetic become new category because they were so varied.
Modal and Tencel is not a kind of material, but a brand.