This is a GREAT thread!!! What a catharsis...
It is my understanding that the term "rope" is used generically, and a rope becomes a "line" when it is being used for a specific purpose on the vessel. For example, a halyard is the name of a particular line, but it is made of rope usually, and if you had a spare coiled up in a bag down belowdecks, you wouldn't necessarily call it a line, you'd call it a red (or green or blue) rope. Halyards are sometimes made of stainless cable (on larger boats) from what I understand, but that also brings up the use of "cable" which I understand can also be made of rope instead of metal...and if you've been in the Navy (which I have not) you probably know when to call something a cable instead of a line or rope...