In Iceland:
Gæludýr (Affection showing/receiving animal) are pets.
Húsdýr (House animal) refers to all domesticated animals, whether pets or livestock.
Búfé (Farm riches/animal) and Búsmali (Farm herdable) is specifically livestock.
In Sweden:
Sällskapsdjur (Companion animal) are pets.
Google Translate says we call them "companion animals" and that the translation is verified by contributors. Might be a regional thing but I've never heard that term.
(Sidenote, what's up with 5 comics with dates ranging between January and March showing up at the end of April?)
@Leonick the five comic update (there actually more) is because for years there where comics that were only on Facebook but now Dayvi put them on the site
...but sometimes we just call them "masters". Especially cats.