Both are some kind of storing mechanisms. Both occupy memory space. But what is the difference between archival of a whatsapp chat and backing up a whatsapp chat?
An archived chat is simply hidden from the Chats tab, which means it requires the same storage space as if it weren't archived. It is meant to be a way to keep your messages organized and don't fill your chats' list. On the other hand chats backup takes all your chats and copies them to a separate file, either on your phone's storage or on the cloud, so that you can restore them in case you loose WhatsApp data or change phone. For more informations go to WhatsApp FAQ.