There are multiple terms around that people use to describe either the dance breaking or people who practise it. The different terms have different origins and we're explaining them right here.
Breaker and breaking
B-Boys, B-Girls, breakers and breaking are all the original, cultural names for anyone who practices the dance of breaking and refers to someone who lives the lifestyle of hip-hop culture.
A B-Boy or B-Girl is the right term for an individual male or female who practices the dance of breaking. Breaker would be a gender-neutral synonym.
The B stands for break, so B-Boys and B-Girls are Break-Boys and Break-Girls.
Some people say that the B stands for Bronx, making it Bronx-Boy or Bronx-Girl. This is in reference to the fact that breaking began in The Bronx borough of New York City.
Breakers is the overall name for a group of B-Boys and B-Girls and breaking is what it's called when breakers are actually dancing. This is because traditionally breakers dance to the break of the track being played. B-Boys and B-Girls were also seen as breaking somewhat emotionally inside when they danced, as they would dance to let out all the frustrations they had from living in the poor, crime-ridden ghettos where breaking and hip-hop culture started.
Breakdancer and breakdancing
The terms breakdancer and breakdancing were coined by the media when they discovered the dance of breaking. Unaware that breakers never put 'dance' on the end of their name and art form, some outlets discovered the kids who were breaking and said they were breakdancing and so called them breakdancers.
With the media and television being the ones who introduced breaking to the world and the general public, the term breakdancer became how B-Boys and B-Girls were first known by everyone outside of hip-hop culture.
Today those who seriously practise the art of breaking and live the hip-hop culture lifestyle have learned the history of the dance and the correct cultural terms of B-Boy, B-Girl, breakers, and breaking. They now use these terms instead of the media-created terms of breakdancer and breakdancing.
But the media still largely uses breakdancer and breakdancing, which is why these terms are still the most common name by which the general public know the dance and the people who practise it.