Starfleet Control was an agency within Starfleet Command that was responsible for maintaining contact with Starfleet vessels and for managing their missions.
In 2267, Captain James T. Kirk requested that Starfleet Control be contacted so that they could be alerted to the position of a black star encountered by the USS Enterprise in the vicinity of Starbase 9. Uhura, however, was unable to contact Starfleet Control on standard Starfleet channels because, unknown to the crew at that moment, the ship had traveled back to 20th century Earth.
Following the Enterprise's return to the 23rd century they were contacted by Starfleet Control, and were informed by Kirk that the Enterprise was home. (TOS: "Tomorrow is Yesterday")
Based on the single reference of this agency, and referenced at a time when the Enterprise appeared to operate under several agencies ("command base", "Starfleet Command", "Spacefleet Command", "United Earth Space Probe Agency"), it is unclear if Starfleet Control was intended to be an alternate name for Starfleet Command, or if it was an agency within Starfleet that maintained the responsibilities similar to modern day mission controls.