Walking a cat is not the same as walking a dog. That’s one of those “Well, duh” statements, isn’t it?
About the only similarity is that there is a human at one end of the leash and a quadruped at the other end. The main objective is totally different. To a cat, the object of the walk is not to find a tree to pee on. Or to see how far or how fast they can go.
When the cat is out for a walk, he likes to move more slowly. Pausing to get the scent of everything. Stopping to sniff the grass; and the weeds; and the trees; and even the sand. He looks around, watching the boats on the river, looking at the birds up in the trees, checking out the bugs crawling around. And he likes to do a little grooming so he will look good to any passers by. But mostly, he just sits.