For paper modelling the most useful glue is PVA. The type used as white school glue. PVA glue is water based, so there are no strong fumes but if over used it can make your paper models go wrinkly. When sticking paper or card you need only a thin layer of glue on one surface. Once your parts are lined up correctly, nip the parts together to make drying quick.
Is glue a tool or a material? Whatever, the glue spreader is a tool – for sure!