What is the key difference between the binomial distribution and the hypergeometric distribution?

The binomial distribution requires a constant and known probability for all trials.

For example, if picking marbles from a bag, the marbles must be returned to the bag to achieve a constant probability (with replacement).

The hypergeometric distribution assumes two different classes of objects, and samples are taken out without replacing back in the "pool" (without replacement).

This is especially useful for small populations without replacement, or events having very small probability.

What is the key difference between the binomial distribution and the hypergeometric distribution?