They may all look like they've been randomly generated, and perhaps, they really are. What differentiates them is their purpose.
Invitation Code = Used to activate a newly created Nine Chronicles Account. You can find the Invitation CodeField after logging in from the Launcher. One-time use only.
Private Key = This is like the Secret PIN of your Bank Cards. Show this to people and you are pretty much doomed. A Private Key is used to gain access to an account, recover an account, and change the account password. Basically, having a Private Key is like having the key to a bank vault.
Nine Chronicles ID = This is widely known as a Cryptocurrency Address to many. It looks similar to Private Keys and Invitation Codes in the sense that they look like an incomprehensible set of randomly generated characters ( I mean, they probably are... Yeah ), but you can differentiate between them because a Nine Chronicles ID will always, always start with 0x. Your Nine Chronicles ID is also used to accept NCG transfers from another player, so it is safe to show to other people. Although, people who has your Nine Chronicles ID can check your account activity through the block explorer.