A cartographic survey, also known as a charting expedition, mapping expedition, mapping mission, or star mapping was a mission whose objective was to make a map of an area. Stellar cartography was a type of mapping.
In 2269, the USS Enterprise went on a mapping mission of the obsolete supernova Arachna. Upon the detection of an intersat code signal from Cepheus, James T. Kirk intended to investigate, leading Leonard McCoy to ask if he seriously planned to abandon the mapping mission to chase a signal which might mean nothing. (TAS: "The Terratin Incident")
In 2366, Jean-Luc Picard asked William T. Riker if he agreed that a mission to the Gamma Erandi Nebula was a "fairly routine mapping mission", which Riker did. Picard, figuring he could afford to miss the mission, sent Riker on shore leave to Betazed with Deanna Troi, who had already requested leave. (TNG: "Ménage à Troi")
According to Doctor Elizabeth Lense, the USS Lexington's mission wound up being less glamorous than Julian Bashir imagined; she described it to him in 2371 as more of a charting expedition than anything else. (DS9: "Explorers")