Morality was the difference between proper and improper intentions. Mores were a set of moral norms or customs derived from generally accepted practices rather than written laws. Ethics were the study of morality in philosophy.
Phlox told Trip Tucker that he was too concerned with his Human morality and cited his decision to join Starfleet as his wish to learn about new cultures when Tucker questioned the concept of Denobulan polygamous relationships. (ENT: "Stigma")
While not completely sane, T'Pol named the Starfleet regulations restraints by Human morality. (ENT: "Bounty")
The Osaarian Orgoth was right when he cited Jonathan Archer's Human morality as the reason he was not able to torture him. (ENT: "Anomaly (ENT)")
Archer later told T'Pol that he did not know much about Vulcan ethics, but Human morality won't let innocent Xindi die. (ENT: "Hatchery")
No Starfleet regulations permitted one's execution without a trial, something Spock reminded James T. Kirk of in 2258 of the alternate reality. The first officer was expressing his concerns about Kirk hunting down and assassining "John Harrison". He also added that a preemptive strike on Qonos was not permissible either. Kirk reminded him that their orders from Admiral Alexander Marcus was not a matter of Starfleet regulation. Spock then reminded him that apart from regulations, the act would be immoral. Kirk then countered that by saying that regulations aside, rescuing Spock from the volcano on Nibiru was moral, yet nobody congratulated him for doing so. (Star Trek Into Darkness)
In 2267, Zefram Cochrane questions the future – the men who have no notion of decency and morality. (TOS: "Metamorphosis")
Janet Wallace later described James T. Kirk as a "man of morality, decency, handsome, and strong." (TOS: "The Deadly Years")
In 2270, Spock believed that Pandronians had a basic language and social structure, and he said that he would assume fairly well-developed mores and traditions as well. (TAS: "Bem")
In 2365, Captain Jean-Luc Picard described in his ship's log the feud between the planets Straleb and Atlec as an ancient morality play. (TNG: "The Outrageous Okona")
Q named the reason he was forced to cover himself with fabric as some outdated Human morality when he chose the Human form in 2366. (TNG: "Deja Q")
The abductingaliens found the concept of morality interesting and named it something they would study further. (TNG: "Allegiance")
After Ambassador Ves Alkar excused his use of Counselor Deanna Troi as a receptacle for unwanted negative emotions as being part of a broader canvas that would help his abilities as a negotiator, Captain Picard responded that he could not explain away a wantonly immoral act as being connected to some higher purpose. (TNG: "Man Of The People")
Captain Picard questioned Q's action while Amanda Rogers was aboard the USS Enterprise-D and accused him of being the "moral guardian of the universe." He further stated that he would pit Human morality against the Q any day and that it was the reason that the Q were fascinated with Humans. (TNG: "True Q")
In 2370, Benjamin Sisko told Jadzia Dax that he did not understand her commitment to the blood oath as it did not fit very well to Curzon Dax's fundamental morality. (DS9: "Blood Oath")
In 2373, Silaran Prin accused Kira Nerys of being a murder as she has no sense of morality. (DS9: "The Darkness and the Light")
Also, that year, Quark told Ishka that the time he lived among Humans – being exposed to their ethics and their morality – was like brainwashing. (DS9: "Ferengi Love Songs")
During the Dominion War, Sisko struggled with himself and his disrespect of the finer points of morality. (DS9: "In the Pale Moonlight")
Captain Kathryn Janeway ordered to put morality aside and decided to let Doctor Crell Moset and The Doctor treat B'Elanna Torres. (VOY: "Nothing Human")
Though Janeway had some problems with the Think Tank members morality, she decided to deal with them. (VOY: "Think Tank")
Janeway's morality was later questioned by The Doctor, Captain Rudolph Ransom, and Valen. (VOY: "Warhead", "Equinox, Part II", "The Void")
In 2381, one of Lieutenant Steve Levy's many conspiracy theories was that the Vendorians put unwitting subjects in morality tests, a theory that actually proved true. (LD: "Caves")