Yes - it’s certainly true that most of the dedicated cordage aboard a ship is not referred to as a ‘rope’.
But Ashley’s point is that there are a number of exceptions, and the phrase “learn the ropes” is current. I was looking for other examples that include ‘rope’ in their name.
My understanding is that any working cordage is a line (or other term). Things like boltropes (a rope attached to the edge of a sail by which it is attached to a mast, boom or other spar) and footropes (ropes under yards on which sailors may stand while working along the yard) are essentially fixed. Therefore, “pull on that rope” is something that sets sailors teeth on edge.
As for other types of lines used in sailing (other than those of the form ‘[descriptive term] line’):
[ul]
[li]Halyards are used to hoist sails[/li][li]Sheets and guys are used to control sails[/li][li]Topping lifts and downhauls are used to raise and lower spars[/li][li]Outhauls and cunninghams are used to control the shape of sails by adjusting their corners on a spar[/li][li]The rode is the anchor line or chain[/li][li]Stays and shrouds are the cables used to support a mast[/li][li]Whipping is small thread or line wrapped around the end of another line so it doesn’t fray[/li][/ul]