The dog we had during my childhood on the farm loved a chase, more than a kill. He was constantly going after something. Like us, a scent can suddenly catch our attention, but then we put some concerted effort into finding a source.
I have memories of seeing him with his nose to the ground every day jig jagging along in search of a chase. It was funny when a fresh scent would come in on a breeze. His nose would point in the air, and he would look like Fred Astaire dancing around for a sense of which direction and what distance. Finally he would check the ground, then back to smelling the breeze. When finally air matched ground, zoom! Off he’d go. He would disappear for a while. When he came back prancy and spirited you could be sure he found some critter he chased as far as he could, until they found some safe spot.
He was a border collie, so his instinct was to chase, but not to kill. He would chase anything he could startle into rapid retreat. I was his cheering section.