I've heard that severe damage to the hippocampus results in the inability to form new memories but still remember old ones. Am I mistaking something? Is the hippocampus responsible for storing memories, creating memories or both?
It's fair to say storing new memories is an important function of the hippocampus. The most famous example is the case of HM https://en.wikipedia.org/wiki/Henry_Molaison, possibly that's where you heard this?
The hippocampus is also heavily involved in navigation, so memory is not the only thing it does, and there are memory systems that don't seem to involve the hippocampus (for example, working memory and motor skill learning. There's some ongoing discussion around how best to classify different kinds of memory, to be able to say more specifically which kinds belong to this hippocampus system). So as always, the story is complicated. But HM's story shows that "severe damage to the hippocampus can result in the inability to form new memories, but still leave old ones intact" is a fair-enough claim.