"Under sail" - literally only sail boats or also valid for boats with engines

I wonder if the expression "under sail" can or should only be used in reference to boats that sail with the wind (i.e. have a sail) or if it could be used for boats and ships as well that move with engine power.

• How would a layman imagine a boat or ship if I'd tell him "We are under sail, heading towards ..."?
• How would a seaman understand it? Is it commonly used to indicate that the ship is moving or that it has a physical sail up?

As an avid boater, I can tell you the correct expression that encompasses both sail and power vessels is under way. The M-W Dictionary even gives it as the first definition:

in motion : not at anchor or aground

Though I would add that a vessel moored to a dock or pier is also not under way.

Meanwhile, the Collins Dictionary indicates clearly that under sail means:

If you cross the sea under sail, you cross it in a ship that has sails rather than an engine.

Note that technically, a vessel adrift and not under command is also under way. To be more specific, if the engine is propelling the vessel, we say under way and making way.

Here's another reference, Skysail Training, where we read that:

Underway: not anchored, or made fast to the shore, or aground. (As defined in Colregs).

Making way: being propelled through the water by sail, machinery, or oar. (Not defined in Colregs)