Driving is the control of the transport usually termed a vehicle. For use of animals it is called riding, principally in reference to horses. Originally driving referred to the occupation of driving working animals. It involves steering to choose the direction and controlling the speed. In transport, driving is moving the driver rather than any passengers necessarily. It also involves stopping and manoeuvring in traffic on roads. Although rare, this could include swimming, diving, skiing, wingsuit skydiving and climbing in theory. These do not use vehicles but are neither freight nor travel.
On mechanised vehicles such as bicycles or cars, it also involves controlling lights and gears. It can also be called piloting for air transport. Or sailing for water transport even though most ships are powered by engines not sails harnessing wind power.
Shipping is use to refer to movement of goods and cargo, or sometimes termed freight. Originally shipping meant by water or sea as this was the predominant form of transport until the 18th Century. Since the advent of railway transport in the 19th Century and road transport in the 20th Century, the term shipping has expanded to include those too. In the postwar period due to advances in aviation, shipping can also include movement by air.
The term travel (in contrast to driving and shipping) means transport of passengers who are not necessarily themselves driving and are not goods or freight. Transport by foot, is one mode that is overwhelmingly generally going to be termed travel rather than driving or shipping (unless using a handcart to move goods). Long distance travel by foot would have even been done in the middle ages as pilgrimages. These days similar long distance walking but for non religious reasons might be called trekking. A person who traveled was known as a traveller.
For travel to and from work is known as commuting.
In the Age of Exploration, Magellan circumnavigated the world by ship. This was travelling rather than shipping but more commonly known as circumnavigation.
Public transport is buses and train provided for passengers from the general public sometimes for a fee for a ticket.