Broke is the state of having no money. Being broke is a distinctly temporary status unlike being poor. You can even be perpetually broke, yet still not poor -- so long as you primarily associate with college students (even if you yourself have dropped out to hit the bong more seriously).
It's GTKY, but an illustration:
When I was born, my parents were broke because my dad was sent to Germany to wage war against the Vietnamese and my mom dropped out of life in the US to follow but couldn't work because she had a baby. When they went home, they went back to college and remained broke until my dad finished his Ph.D. and got an associate professorship at Washington University. We were not poor because my parents came from solid middle class stock and knew what to do with money at least well enough to tread water in the rat race.