Both OMNI and Counterparty run on Bitcoin as layer 2 protocols without a sidechain.
Don't know about OMNI, but doesn't Counterparty require you to burn bitcoin? Isn't it more like a transitioning to another currency, rather than just creation of currency?
IIRC Counterparty burned bitcoins for the initial distribution of their XCP token, maybe they've burned more coins since then but that's beside the point. When I refer to OMNI and Counterparty creating a currency of their own I don't mean their native tokens (if you can call them that) but I mean the tokens that are created using those native tokens. USDT in the case of OMNI.... and... sigh... Rare Pepes in the case of Counterparty, for example. The denomination, amount, value etc. of these tokens being largely independent of the value of the Bitcoin transactions underneath.
Liquid is just one example though. Rootstock on the other hand uses merged mining. That is the say, since sidechains use blockchains of their own they can run on all sorts of consensus algorithms, including PoW-based ones.
Correct. Rootstock isn't trust requiring. So, what's the broad distinction between L2 and sidechain?
Like I said above: I think the clearest distinction is that sidechains run on separate blockchains while layer 2 solutions in general not necessarily require one.
Or another view: Layer 2 can be seen like the layers of the OSI model, eg. HTTP running on top of TCP/IP (I believe that this is even the root of the L2 nomenclature in the first place?) while sidechains connected to a main chain can be compared to LANs connected to the Internet. Fun thing is this analogy even accounts for LANs requiring protocol layers on top of the base layer to function, just as sidechains need more than just basic transactions.
The true second layer would allow locking for example 1 BTC, and splitting it between thousands of channels, without any on-chain transactions. Also, because of that bottleneck, you cannot build another layer on top of LN, because it would still require on-chain interaction.
I believe what you are describing is pretty much what is described in the channel factory proposal for a potential layer between LN and the base layer:
https://tik-old.ee.ethz.ch/file//a20a865ce40d40c8f942cf206a7cba96/Scalable_Funding_Of_Blockchain_Micropayment_Networks%20(1).pdfApart from that I believe you can still add another layer on top of LN in the form of colored coins via LN? Though the viability of that seems to be controversial.
And if we also introduce the State channels in the comparison? I deduce that they are pay channels. Are they not the same as an atomic swap?
No, atomic swaps take place across blockchains.