There are lots of different specialty papers in use today. Photographic papers qualify as specialty papers, given that they are fairly streamlined in terms of their purpose. Specialty papers are common for photographers and a lot of other artists. The light-sensitive chemical formula used to coat the papers reacts with the chemicals used for processing photographs producing some very high quality prints.
A lot of photographers swear that the quality of the picture is better for the people who use photographic papers and who create the prints themselves. The photographic papers are layered with a sort of chemical that is sensitive to light, and this is what allows the photographic papers to work as well as they do for so many people.
Artists will use certain types of paper for sketches, certain types for watercolours, and other types of paper for almost all of the other types of media that people will usually imagine. Even different pencils require different types of paper in many cases.
Certain professionals use specialty papers. Graphing paper is common for engineers and architects, for instance, even in a world where they do a lot of their work digitally. Other professionals are going to have their own special paper that is made in order to conform to specific requirements, and few other people will use these niche pieces of paper.