According to ancient Greeks (that is, Greeks who have long been dead, not Greeks who look like they should have long been dead), alyssum is a place in heaven reserved for average, everyday, undistinguished and virtually indistinguishable people. Alyssum contrasts with Elysium or the Elysium fields, which, again according to ancient Greeks, is a spot in heaven reserved for heroes and people who had an in with one or more of the Gods (in heaven, it’s all about who you know). Because alyssum is for the ordinary man (and presumably the ordinary woman as well, but the literature is silent on that point) its name is always lower-cased to denote its lower place in the heaven hierarchy, whereas Elysium, which is reserved for heroes and god-groupies, is always capitalized.
In truth, the structure of alyssum is not all that much different from Elysium, but there are some significant differences in the personal experiences one has in each. The food is way better in Elysium. There is also almost unlimited free booze in Elysium, whereas if you’re in alyssum for the long haul you might, at most, get a glass or two of free wine or bear, but for short stays you have to pay for your alcohol.
You also get a lot more personal space in Elysium.
In addition, in alyssum you have to spend your time sitting in a chair that reclines only slightly—and in some locations in alyssum the chairs don’t recline at all. In contrast, for long-haul stays in Elysium you get a chair that, at a push of a button, unfolds into a lie-flat bed.
If you’ve got to die anyway—and you do—you should definitely try to butter up one of the gods and get yourself upgraded from alyssum to Elysium. Unfortunately, the cost is far out of the reach of most people unless the gods see fit to award them free upgrades, and the gods have been cutting way down on that lately.