[theshrike79]

Statistically, cats are really bad at catching mice. They might catch one, maybe kill it, maybe not. Maybe they'll just play with it and let it go.

Terriers on the other hand... https://youtu.be/l2Pyu-Cj0gg

[TulliusCicero]

Maybe them being around still scares the mice enough?

[jyounker]

The cat doesn't have to actually catch the mice and rats, as they are instinctively afraid of the smell of cat urine, even in small amounts.