(written from a Production point of view)
Arcturus is a real star described as the densely populated homeworld of the Arcturians. (The Making of Star Trek: The Motion Picture, pp. 131; Star Trek: The Magazine Volume 2, Issue 9, "Who is that Alien?", January 2002)
In an early story outline for TOS: "The Cage" (29 June 1964), when the lead was still Robert April, the captive creatures kept by the Talosians in their zoo-menagerie included something a race that was reminiscent of a "civilization April himself has seen –the intelligent Lemur-life of a Class M planet in the Arcturus system." (The Making of Star Trek, p. 59)
According to Star Trek: Star Charts ("United Federation of Planets I") and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), the Arcturus (Alpha Boötis) system was located in the Alpha Quadrant. The primary was a K-class star. A planet in this system was known as Arcturus, which was a Federation member in the late 24th century.