Do ships travel in a 'curved' line?

I know when a plane route is drawn on a map it appears 'curved' but is really straight, so ships also go in such a 'curve'?

If you draw the track of a ship at sea, it will appear curved because of the optical illusion of tracing a route on a globe of the earth and then laying it out flat... but the ship, like the plane, is actually going straight.

You should be asking this in the Geography section so someone can explain Mercator Projections to you.