Our cats will chase squirrels and defend their territory... if provoked. Normally they share space with teh squirrels in the yard while they are bird watching.

Many years ago, we had three cats and one mouse. The mouse would run the baseboard in the living room (via dining room and kitchen). One cat followed along, about a foot behind the mouse. A second cat was in the middle of the room, playing with a toy mouse. The third cat went it into hiding.

I caught and ejected the mouse in a shoebox.

(All of the above creatures have passed on.)

This can depend on how long they spent with their Mom's. One of mine knows how to hunt and proved it more than once with mice that got inside during the winter. (Eww).

The other two just look rather perplexed and don't know what to do. They're absolutely entranced watching Raz when he's in action though.
They'd help out if they could. But not a clue.

Both of them were separated from their Mums way too soon - that much of their background I do know. One at 8 weeks and one right around there. Not old enough to learn to hunt.

Apparently Raz got his training in where he lived before he was rescued. I think he was under a year old when the shelter took him in from an outdoor hoard. But he obviously spent time with his Mum. You'd never think a cat the size of fridge could move that fast either?

I'm glad you were able to usher the critter back out. That would be my preferred method for everything that wanders in from outside!

Protecting property seems to be different than home invasions.

When my cats bring me furry creatures, they are already uncoaxable.

Brave until they realize that the thing making the noise is real.