But the first one is more synonymous with "tantalizing" news. The second one would be more akin to "recently developing" news. Although in normal usage they would be interchangeable nearly all of the time.
Yes, there is a difference, although a piece of news may be both.
Hot news is current news of significant or wide interest. Breaking news is news reported while an event is ongoing.
One recent afternoon, for example, New York radio and TV programs were interrupted for the report of the breaking news (so stated by the reporters) that a helicopter had just crashed into a river here in the city and rescue crews were on the way. Later, after four of the five people on board had been rescued and an investigation had begun into the cause of the crash, it was still hot news, but it was no longer breaking news.