Is there any word for “driving” a boat?

The activity of driving the boat is likely regularly called "piloting the boat". You may likewise hear individuals say "directing the boat," exploring the boat" or a lesser-known "conning the boat. Yet, the basic term is "Piloting".

  If it is your own, private vessel, you can say what you want.

"Sailing" is sufficient  for crewing on,  commanding, and/or  steering a vessel; powered or not.

  You can call your 15' Sunfish a "ship", or  an "it",  even,   if you  wish.

  Technically; "Piloting" doesn't mean steering, control, or command of a vessel; like an Airplane's Pilot would. It means usage of  an external man  to guide  vessel  thru shoals, reefs,  or to a berthage.

The person who is in actual control of the direction of travel is called the "Helmsman". If it is a small boat the person might also be called the captain. On a ship (a vessel of greater then 100 foot keel) the Captain gives the orders to the helmsman and also to the engine room telegrapher. Even on a "crew racing boat" (a row boat) the tiller is controlled by the helmsman. On a row boat with just one rower, a second person might sit where they can see a head of the boat to direct the person rowing and is called the helmsman.

I think “sailing” applies to all sorts of boats not just sailing boats.

Not that I know of. In general terms, you can just call it steering a boat or a ship. There are more ways you can describe it, such as saying that someone is at the wheel or at the helm of a boat, or at the tiller if the boat has a tiller.

If you want to be poetic, you can say that someone is piloting a boat, but in some circumstances that could be misleading since a pilot has a specific function in marine situations; it's a person who has detailed knowledge of a port and is taken on board when a boat or ship is approaching that port, solely for the purpose of making sure the vessel gets into port safely.

If you say that John is sailing a boat, that almost always means John is steering it. If you say that John and Mary are sailing today, that doesn't say who is steering the boat.

coxwain steers a boat or ship, captain is in charge, pilot is taken aboard for entering/leaving ports, skipper is a generic term for the person in charge

THAT IST DRIVING AN BOAT: AN DIFFERENT TYPE OF VEHICLE THAT IST CONTROLLED BY THE DRIVER:

One pilots a vessel, captains a vessel, navigates a vessel, as well as sails, paddles, rows, motors, steers and commands.

Sailing - sailboat

Piloting - a powered water vessel

Operating is another term used.

navigating, steering, sailing, operating