Today, I think of a Stalking Rifle, in my mind, as being akin to a mountain hunting rifle.

Lightish.

A bolt action or a single shot. Kipplauf etc.

A suitable cartridge chamering. It might have a 'magnum' powered chambering these days.

Longish barrel. 24 inches to 26 inches.

Scoped. A modern mountain rifle might have a greater powered scope.

Classically styled. For the type of rifle it is.

A stalking rifle like this, for me, might be a .275 Rigby M98.

Or perhaps a 7mm SEvH Kipplauf.

Or something else.