A print was an impression, image, or scan of the shape and texture of a part of one's body or the graphical representation of an individual or species' identifying characteristic, used for identifying purposes. It could be left behind as part of one's normal activities (ENT: "Stigma") or recorded on purpose as part of one's records, a confirmation procedure matched against same (TAS: "The Survivor") or authorization for access to classified information. (Star Trek II: The Wrath of Khan)
A mark was another name for an impression left behind by an object. In 2365, while playing the role of Sherlock Holmes in the holodeck program Sherlock Holmes Program 3A, Data noted the evenly-spaced marks on a murder victim's neck, which he claimed were as unique as fingerprints, and concluded that the man's common law wife had garroted him with her beaded shawl. (TNG: "Elementary, Dear Data")