Why was the single war between the Republic and The CIS called "The Clone Wars"?

Both Clones Wars tv series as well as the movie refers to the events as the "Clone Wars", as does Leia Organa.

However, there was only one three year war between the Galactic Republic and Confederacy of Independent Systems.

At the end of Star Wars II: Attack of the Clones, Yoda refers to it as "The Clone War".

In Star Wars IV: A New Hope, Leia refers to Kenobi has "having served her father in the Clone Wars". This seems to be a continuity issue with later canon material, since Bail Organa was a Senator in the Galactic Republic, and the Jedi served the Chancellor. I am under the assumption at the time of the first movie, Lucas thought about having more than one actual war involving clones, but decided to change it later.

Is the use of the plurarized "wars" in the title of the movie and two tv series simply a matter of referring to Leia's original phraseology?