They are bitcoins, many people don't understand that and try to prove that Bitcoin with LN is not a real Bitcoin because it doesn't use normal coins.
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There are no Lightning Network tokens. Each party is transacting with each other without broadcasting anything to the Bitcoin network. Everything is settled down once someone decides to close the channel. The biggest issue right now is that channel limits how much you can spend. Split payments are a planned feature.
I think though there is a reasonable case to be made that lightning network obligations are not bitcoin because one can not send those obligations to a bitcoin address. That which can be sent to a bitcoin address is not an unreasonable definition for the world bitcoin bitcoin, I think.
I suppose a good analogy is checkbook money. Technically not the same thing as cash or base money but people chose not to differentiate. They just call the checkbook money they have on balance "dollars" even though they obviously are not literally dollars.
I don't really get "the problem" you mentioned. That's how I think it worked: 1. Someone created a node and decided to open a channel with that node 2. Bitcoins were sent to a multi-signature address which private keys are in control of both parties. 3. Someone else opened the channel to the same node and it was possible to start sending transactions across decentralized LN network.
Ah yea I get it. It's because the entity that I am opening my channel with has the opposite balance with respect to me that I have with respect to him. We don't both have positive balances to each other. Haha. Dumb.
The android wallet that I'm using doesn't seem to have the functionality to open a channel where I am the creditor and my partner is the debtor. In other words a channel that I can receive funds on without having spent down first. But just because this wallet lacks that functionality doesn't mean the network lacks that functionality. Tell me if I got something wrong here.