The difference between normal and binomial distribution is that normal distribution in statistics refers to a data set in which the probability of the outcomes of the events are closer to the average value. Examples include blood samples, IQ scores, etc.
This means, the more the tests, the closer the outcomes are to the average.
Binomial distribution is when the probability of the outcome of an event is either positive or negative (pass or fail etc.). E.g., tossing a coin, rolling a die, etc.
The binomial distribution shows the possibility of an event succeeding or failing. For example. The possibility of a 6 when rolling a die is 1/6.