They are actually quite different games. Ultimate Werewolf is a version of the party game known more widely as simply Werewolf, or Mafia. In its most basic form, there is an informed minority (the titular werewolves or mafia) and an uninformed majority (the town). The game is played over several rounds, or Days (or Day/Night cycles to be more accurate), where each Day everyone votes on a player to eliminate via lynch and each night the werewolves choose a (non-werewolf) player to eliminate via a "night kill", which then repeats until one side has eliminated the threat of the other. It generally requires a moderator who knows the roles of all players, especially when some players may have additional powers (such as a seer who can find out whether another player is town or werewolf, or a doctor who can save someone from being killed at night).
ONUW is a game that is essentially played in a single round, with the aim of distilling a lot of the discussion and voting of Werewolf and removing the player elimination factor. In addition, it adds roles that mean that players may not be entirely sure of their role once discussion starts. It still has the informed minority versus the uninformed majority, but it then takes things in quite a different direction and it contains some very different roles (as well as some similar ones).
Technically, you could possibly use the role cards from one to play the other, but you'd then need to know enough of the rules to explain what each role actually does since the card's text would often be completely inaccurate for what the role does in the other game.