'Memory' isn't one system — it's several, with different capacities and mechanisms. Short-term memory holds a small amount of information briefly (classically estimated around 7±2 items by psychologist George Miller in a famous 1956 paper, though modern estimates for pure capacity are closer to 4). Working memory is related but distinct: it's the active manipulation of held information (doing mental math, following multi-step instructions), relying heavily on the prefrontal cortex, and it's much more capacity-limited and effortful than short-term storage alone. Long-term memory, consolidated primarily via the hippocampus, has effectively vast capacity but requires the information to be encoded and consolidated — most short-term information never makes that transition at all.
The case of patient Henry Molaison (known for decades in research literature only as "H.M.") demonstrated this separation dramatically: after surgery to treat severe epilepsy removed his hippocampus in 1953, H.M. could hold a conversation normally (short-term/working memory intact) but could never form a single new long-term memory for the rest of his life — meeting the same researcher daily for years without ever recognizing them. His case became one of the most studied in neuroscience precisely because it proved these are genuinely separate systems, not one memory store operating at different speeds.