As the settlement grows, transportation and mobility requirements will grow. From simply walking from one area to another, delivery and transport vehicles will be required for heavy loads. As distances grow longer, for example from a spaceport to a living area, or from a deep tunnel settlement to a surface greenhouse.
Walking on Mars should be possible, and less hard on the knees. Some adjustment will be required as inertia will remain the same but weight will go down, so cornering at high speeds will take new skills. Good planning should prevent some of the errors of recent urbanism while promoting the good points of walkable cities and communities.
There is no point to introducing hydrocarbon burning vehicles to Martian cities. Small delivery vehicles as well as pallet loaders should appear fairly soon in the colony history. Electrical self driving vehicles should be a reality by the time a martian settlement is built, and could serve in a form similar to what has been proposed by The Boring Company of Elon Musk.