broke means no money at all. poor means not much money. Broke is basically extremely poor. Not everyone who is poor is broke, but one cannot be rich and broke at the same time. Some rich folks like to pretend they are broke, but they aren't. Not having some cash on hand is not the same as being truly broke. One can, however, be "broke" at the moment, in the idea of "I have no cash money". Lots of people are broke the night before their regular payday, but they are not truly broke, only cash-deprived for the moment. They are not broke once they get their paycheck the next day.
Broke can be used for either: truly lacking anything of value, and temporarily having no cash or money to spend at the specific time.