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Love the subtle point you are making. I think people use the L2 analogy because they either are just repeating what they have heard or they are trying to communicate to people that understand fiat payment systems.

One of the things that people do not understand in addition to this is that their fiat money, credit cards, and checks are not bearer assets in the way bitcoin is. During the gold standard era one could take cash and exchange it for gold. When I realized what bitcoin was, a digital money that is also a bearer asset it blew my mind. When I realized I could run my own node it blew my mind. When I realized I could run a lightning node and basically provide a BETTER and bearer asset version of an L2 it blew my mind. But I thought of it as an L2. And you are right. Its really not like the Credit card networks or "traditional" L2s. That's selling Lightning way too short.