Is it true that heavy vaginal discharge the same as bacterial vaginosis?

Not necessarily: Bacterial vaginosis is a specific type of vaginal infection that women get, and is quite common. A heavy vaginal discharge simply means there is a lot of discharge from the vagina, but that doesn't say why the discharge is heavy. It could be heavy due to a vaginal infection such as yeast or bacterial vaginosis, but from something irritating them, or from using a vaginal medication for instance.