Stroll (noun) to stroll, to take a stroll (verb) to walk in a slow relaxed way. This is associated with pleasure, more than sport and adventure, and so it would be perfect to describe a walk around the park.
To wander is similar, but refers less to the way you walk, than to why and where:
‘Terry has gone for a wander,’ would make the listener think that he has, perhaps, decided to explore an unknown area, and implies adventure.
Similarly; ‘Helen has wandered off,’ sounds as if Helen as got lost.
There are many more verbs to describe walking in English, some of which are important to know.
To hike is very energetic walking, normally in the country with a strong pair of boots.
To hitch-hike doesn’t mean to walk at all, but means to stand at the side of the road with your thumb in the air, waiting for someone to give you a free ride in their car. (Note that the European Autostop doesn’t exist in English. Neither does footing - for this we say to jog.
To stagger is to walk in an irregular way. Very typical if you drink too much.
To swagger is to walk when you think you are the coolest and the greatest.
To hobble / to limp means you have a walking difficulty, injury or handicap.
To march is the military way of walking.
To goose step is the fascist military way of walking.
To tiptoe is to walk on the tips (points of your toes), probably to be silent.
To creep is a similar verb meaning secretive silent walking.
To hop is to walk on one leg.
Watch this space. More coming tomorrow.