Library: a stateless code pattern/schema. The success of a library can be measured by the number of times it is copy/pasted, replicated, re-deployed, and custom tuned. This is the tested and true thing that open source does well. Examples: Linux, ERC721. But as the history of open source shows, monetizing a library is often done indirectly. Usually it comes from building commercial services on top.
Network: networks are stateful, singleton, canonical – where the presence of those properties create network effects. Stateful networks have traditionally been closed. Examples: Facebook, Twitter. That's because a company has been required to maintain the state, and there’s a cost to doing that. Crypto changes that because it's now possible to incentivize independent parties to maintain state, because we can incentivize them with tokens! That's what blockchains do, and they are the obvious example of open, stateful networks. Their state is singleton (due to global consensus) and canonical (due to social consensus.) On top of blockchains, we can build stateful networks at the application layer too. Networks can be formed around the state in a singleton smart contract, or an application-specific rollup. An example is Uniswap, whose state is liquidity in a marketplace (tokens that are deposited to Uniswap’s smart contracts.) That state has network effects because the more state (liquidity) the better the pricing for exchange.
What is the point of this framework?
Building (and monetizing) open source libraries is a tested and true strategy, but crypto presents a new opportunity—to build open, stateful networks. In my opinion, that's the exciting opportunity and where the most value creation will be. If you’re setting out to build something in crypto, ask yourself: is it a library or an open, stateful network? We need both, but the max interestingness and value creation is probably in the new thing: open, stateful networks.