I've been tossing a few ideas around for a new
topic of discussion and came up with this one.

Your thoughts please?

That's easy

An exchange of diverging or opposite views is an argument but typically becomes a quarrel when it becomes a heated or angry one

In "The Enemies of an Open Society" Karl Popper recommends not taking up time discussing definitions if they are unnecessary to get to the meat of the question. He gives as an example a problem given to investigate the behaviour of sand dunes. Instead of defining a sand dune the investigator would set out to study mounds of sand between one and one hundred meters.

I hope the above is an argument and not a quarrel.

Desmond Tutu once stated - "Don't raise your voice,
improve your argument."

With that thought in mind, I've come across an
interesting site on the web which tells us that -

Stephen Toulman, an English philosopher and logician,
identified elements of a persuasive argument. These
give useful categories by which an argument can be
analyzed.

The first element that Toulman lists is "the claim".
He tells us that many people start with a claim then
find that it is challenged. You're asked to prove
your claim and you have to provide grounds (or data)
and hard facts plus the reasoning behind the claim.
Grounds are the second element listed and they may
also include proof of expertise and the basic premises
on which the rest of the argument is built.

Anyway the site is worth a read:

http://changingminds.org/disciplines/argument/making_argument/toulman.htm

Possibly no difference at all (especially in the context of many OLO political discussions) -

argument /noun: an exchange of diverging or opposite views, typically a heated or angry one.

synonyms: quarrel, disagreement, squabble, fight, difference of opinion, dispute, wrangle, clash, altercation, feud, dissension, war of words, contretemps, exchange of views

quarrel1 / noun: an angry argument or disagreement.

synonyms: argument, row, fight, disagreement, difference of opinion, dissension

Foxy glad to see you back posting.

Not dictionary definitions but I tend to think of an argument as broadly about a single topic or issue and a quarrel as covering all bases and being more about the conflict than the actual disagreement.

R0bert