'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.
After surgeons removed most of H.M.'s hippocampus on both sides of his brain to control severe epilepsy, he could hold a completely normal conversation, do mental arithmetic, and follow multi-step instructions given moment to moment — his short-term and working memory were fully intact. But he never formed a single new long-term memory for the rest of his life. Researcher Brenda Milner, who studied him for decades, would introduce herself to him fresh at the start of every single session, year after year, because he retained no memory of ever having met her before, no matter how many hundreds of times they'd actually spoken.