A breed or variety was a specific type of animal, plant, or robot. One who bred lifeforms was called a breeder.
In 2365, when a holodeck computer on USS Enterprise-D asked Jean-Luc Picard which breed of horse he wished to add to his holoprogram, he answered, "Arabian". (TNG: "Pen Pals")
In 2367, Data surprised Jenna D'Sora with a bouquet of flowers that were a variety of crystilia. (TNG: "In Theory")
In 2372, Tuvok identified a flower as "a rare variety of Cypripedium, of the Asiatic genus Paphiopedilum". (VOY: "Tattoo")
Also that year, USS Voyager's sensors located a variety of orchid that was believed to potentially be a nutritional supplement. (VOY: "Tuvix")
In 2373, Q proposed mating with Captain Kathryn Janeway to create a new breed of the Q species which would have the combined omnipotence and infinite intellect of Q with the best that Humanity had to offer. (VOY: "The Q and the Grey")
That same year, Grand Nagus Zek decided to fund research into a new breed of Hupyrian beetles, as he felt they would "revolutionize the entire beetle snuff industry."(DS9: "Ferengi Love Songs")