In general, hot-press papers are smooth whereas cold-press papers are slightly textured.
"Handmade paper with a smooth finish is described as hot pressed or H.P.. The term is not strictly accurate, for papermakers achieve this particular finish in a variety of ways: the sheets may indeed by pressed between heated glazing rollers, but they may also be passed through cold, highly polished metal rollers with pressure; historically the surface was obtained by polishing with a smooth hard object such as an agate or other stone." (Turner, The Book of Fine Paper, 34.)
Cold-press papers are often referred to as NOT (all caps) for not hot-pressed. "It describes a surface which is the result of parting and re-pressing handmade sheets wihtout any intermediary felts or boards. The finish is slightly textured..." (Turner, 33.)
Digital paper manufacturers and the digital photography industry have further loosened the terms to mean either textured or smooth.