A vegetarian excluded any meat-based foods from their diets, either as a personal choice or as part of their culture. They are not to be confused with herbivores, whose natural diet consisted solely of plant-based foods. Though a vegetarian diet might be seen as a more moral choice (as opposed to eating slaughtered meat), it was once noted by Spock that, as plants are living organisms, vegetarians and meat-eaters alike feed on death. (TOS: "Wolf in the Fold")
By 2364, Humans no longer enslaved animals for food purposes, although "meat" remained available, and continued to be eaten, in the form of the inorganically materialized output of replicators. An Anticanambassador, who insisted on slaughtering live animals for food, considered this practice to to be "sickening" and "barbaric." (TNG: "Lonely Among Us")
The preference for keeping live animals by the Human colonists on Omicron Ceti III a century earlier suggests the practice was abandoned sometime between those two points.