What each kind of exercise does
Physical exercise builds fitness, keeps joints and muscles working, and helps with weight and heart health. Dogs need it. How much depends on age, breed, health and fitness.
Mental exercise uses the brain. It includes sniffing, problem solving, learning new skills and exploring new places. It gives the dog a chance to think, choose and succeed. It also helps meet natural needs like searching and foraging.
They overlap. A sniff walk is both. A game of fetch has some thinking in it. But they are not the same thing, and one does not replace the other.
Think of it as a menu, not a contest. Some days your dog needs more movement. Other days they need more thinking. The skill is noticing which one, and that comes from watching your dog after the activity, not during it.
If you only have ten minutes on a busy day, spend them on a sniff and a short search. It is a small habit with a big return for most dogs.