Let's start with the question:
What is discussion?
A problem is decided upon, the parties will talk about the problem, and try to come up with possible solutions.

What is a debate?
According to World Book Encyclopedia, 1988 Edition
". . . is a series of formal spoken arguments for and against a definite proposal"

What does this all mean ?

Debate . . . In other words, at least two people get together to figure out who's "solution" to the problem is the best.

Is Debating Arguing?
. . . not if organized.  If organized, there will be two sides with the same number of participants on each side.  Sometimes a moderator will run the debate, to make sure both sides take turns and one side doesn't get more time than the other.  Sometimes Presidents will go on TV and debate each other, such as Kennedy and Nixon in the first televised debate.

Where and why do Debates Occur now?
Many "debates" are organized in governments, schools and other places.  Many high schools and colleges have "Debate Clubs."  Political debates, environmental debates, and about any subject debates can occur.

Abraham Lincoln had given a fired-up speech called the "A house divided against itself cannot stand speech" at Springfield earlier in '58.  This speech caused a big stir in Illinois, and in the nation.  Some thought such an idea of stopping slavery, or ridding the country of slavery would cause a division in the country and perhaps a civil war.

Abraham Lincoln gave a few more speeches and then Challenged Douglas to a series of debates.  There would be seven debates at seven different Illinois cities, all over the state.

Each candidate, Lincoln and Douglas would speak for 1 and 1/2 hours.  That was the format of this famous debate.  Lots of people showed up at all, but the debate at Jonesboro, the southern end of the state.

Lincoln and Douglas agreed on one point:  slavery was in the southern states, and neither of them had a desire to bring it to an end.  Lincoln believed in keeping the nation whole.  Douglas was very adamant that the blacks were a lesser race, and had no place in white society.  At times, it seems Lincoln felt the same way, but Lincoln would end up stressing that all humans deserved the right to be free.  Enslavement was an abomination to Abraham Lincoln.  He kind of represents the very beginnings of the establishment of a totally free United States, and equality among all people.