A debate is a formal discussion on a particular topic, in which opposing
arguments are put forward. Debates occur in public meetings, academic institutions, and legislative assemblies.
A leaders’ debate or Presidential debate is a public debate (everyone can watch) held during a general election campaign, where the candidates express their political opinions and public policy outlook, and their take on them, to prospective voters.
All the presidential debates have a moderator.
The first official US Presidential debate took place in 1960 between the then U.S. Senator John F. Kennedy, the Democratic nominee, and Vice President Richard Nixon, the Republican nominee, in Chicago.
This year, as the US elections are scheduled in November, the presidential debates are taking place between incumbent Donald Trump, Republican nominee, and former Vice President Joe Biden, the Democratic nominee.
In USA, there are only 2 parties who can fight elections. They are called the Republican Party and the Democratic Party. Such a system is called, predictably, the Two-Party system.
In India, any number of political parties can be registered and they can fight elections. That is why you see multiple signs in the polling booth.