I read terms
binary data and
binomial data in a textbook. What's the difference between them?
Possibly what is meant is that binary data consists only of 0's and 1's for "failures" and "successes" (notice that what you consider as a "success" is arbitrary) and follows a Bernoulli distribution. Binomial data is data that emerged after observing $n$ Bernoulli trials, i.e. it is a sum of Bernoulli random variables and it consists of non-negative integers, it follows a binomial distribution. I say "possibly" because this should be defined in your textbook and it is the only reference that tells you what the author meant.