People who suffer from bulimia nervosa experience binge-eating episodes which are followed by "purging" as it is called, meaning that people who suffer from bulimia nervosa will first eat huge amounts of food and wll later vomit this food out as to prevent weight gain.
Binge-eating on the other hand is similar in the sense that people who suffer from this eat a lot of food but do not "purge" afterwards; they just eat huge amounts of food. People who suffer from binge-eating can gain a lot of weiht in short periods of time.