With replacement
The pool resets after every draw
If an item is returned before the next draw, the probability stays the same from one draw to the next. That is why with-replacement setups often fit repeated-trial models like the binomial distribution.
Without replacement
The pool changes after every draw
If an item is not returned, the next draw comes from a smaller pool with changed composition. Card hands and sampled batches fit this pattern, which is why they lead to hypergeometric probability instead of binomial probability.
Independence
Replacement and independence are closely related
With replacement often preserves independence because one draw does not change the next one. Without replacement breaks that independence because the population changes after every draw.