Are there different types of reefs?

Being from NJ and not well traveled I do not have a lot of experience surfing reefs. I am asking this question because as we all know surfing reef is dangerous compared to NJ beach breaks because reefs are hard and sharp. Although, it appears that not all reefs are sharp and dangerous. I say this because you often see videos of people standing on reefs or "bouncing off the reef" and not significantly injuring them selves.

I know from my limited experience surfing reefs in the Caribbean, everyone said "DONT NOT STEP ON THE REEF, DONT NOT HIT the REEF!" because of urchins etc. Are reefs in Hawaii drastically different then reefs in the Caribbean, and Australia?

Maybe someone well traveled, or a marine biologist can help out

Thanks all.