Is a key lime pie an actual pie? To me a pie has to be enclosed in pastry (shortcrust, puff, filo) top and bottom. If it is enclosed in suet or made with suet, then it’s a pudding. If it has only pastry on the base and sides, it is a tart. Cake doesn’t have any pastry, so includes things like cheesecake because the base is made of crumbs rather than pastry.