This is not yet another ICO where some coin is launched, this is the turning point for one established platform to deliver another. And this new platform is, by definition, going to host eventually many different coins because it is a multi-blockchain platform.
NXT, that was born in 2013, is the platform where Ardor was designed and from which it was developed. And it also is used to set the initial distribution of tokens for the new platform.
ARDR will be the main chain token of the Ardor platform. And before it runs on its own blockchain (starting January 1st, with the launch and the Ardor genesis block) it has been initially distributed on, and traded on, the NXT platform as an NXT asset.
And IGNIS is the token for the first child chain (or sub-chain, or whatever you prefer to name it for clarity) that will be hard-coded in the Ardor platform at launch. While the main chain, and ARDR, will be only used to secure the whole platform and generate the new blocks in the chain, IGNIS can be used for all the other things that its predecessor, NXT, can do: issue assets and currencies, send messages, cast votes, define smart transactions, sell digital goods, etcetera. All these features will also be available for any additional child chains that Ardor might include in the future.
The only naming that may appear as unnecessarily confusing is the JLRDA token, a currency in the NXT blockchain that the developers are using for half of the distribution of the future IGNIS coin, the half sold in the ICO. It would have seemed easier for them to use the same name for the token, IGNIS. But I suspect that, if they did not do it this way, it was because the code name IGNIS was already used for a currency in the Nxt monetary system. Or squatted by someone who moved fast and wanted to exploit it. Since these token names cannot be duplicated, the developers had to go for a different token name for the sale.
I understand that this scenario is more complex than other ones you may have seen for other projects being born, but hopefully what I explained can help you to understand that there's reasons behind the apparent complexity.