Are you talking about M'Ress? She was a Caitian. Roddenberry actually tried to get Majel Barret to play her in the motion picture, but she didn't feel like wearing Cat makeup. They did have several cat-like humanoids throughout the movies that are supposed to be Caitian (although their name wasn't actually mentioned).
The Kzinti were borrowed from another sci fi series, since the writer of that series wrote the episode. Basically, Earth fought a war with them a long time ago and won, so the Kzinti have been demilitarized and only allowed to have small police ships.
The Lyrans were invented for Starfleet Battles and I believe are supposed to be related to the Kzinti (although they hate each other and would probably kill you if you suggested that). The Mirak from Starfleet Command are the Kzinti, renamed for legal reasons.
CaitiansKzinti