Definition of Probability Distribution:
A probability distribution is a table or an equation that links each outcome of a statistical experiment with its probability of occurrence.
Definition of Binomial Probability Distribution:
A binomial distribution is a specific probability distribution which is used to model the probability of obtaining one of two outcomes, a certain number of times (k), out of fixed number of trials (N) of a discrete random event.
Are there two definitions consistent with each other? I think no.
Why? Because, how is a Binomial Distribution acting like a table or equation that links each out come of the experiment with its probability of occurrence?