Insecurity was the state of being unsure of one's own abilities and worthiness, while an insecurity was anything one felt insecure about.
In 2268, Leonard McCoy attributed Spock's not being afraid to die as being due to his fear of living, as every day he lived would be one more day to allow his Human side to show. He felt Spock was insecure and would be unable to process real feelings. (TOS: "Bread and Circuses")
In 2365, Geordi La Forge believed Data was exhibiting insecurity. (TNG: "The Schizoid Man")
In 2373, while controlling the body of Kes, Tieran asked Tuvok if the Vulcan really believed he could hide his fears and insecurities from him. (VOY: "Warlord")