and vise versa?
Aw, Jeez. Now, I’ve got John The Ruminator running through my head.
No. Informally, ungulates are any mammal with hooves, and there are plenty of hooved mammals which are not ruminants. Horses, for example.
Formally, ungulates are members of the clade Ungulatomorpha, which includes the familiar hooved mammals (both perissodactyls [horses, tapirs, rhinos], and artiodactyls [most other hooved forms, except hippos and pigs]), but also includes cetaceans, manatees and elephants. Ruminantia (ruminants) is a subclade of Artiodactyla, and includes giraffes, Bovoidea and Cervoidea.
Bovoidea = cows and relatives
Cervoidea = deer and relatives