Today blockchains like Bitcoin or Ethereum are named as examples of successful decentralisation. These large infrastructure projects are not local-first since their purpose is to establish global consensus on who owns what — this question requires a connection to the global network to be answered.
An even more important distinguishing characteristic is the efficiency of resource usage. With the current state of the art in consensus blockchains vast amounts of energy need to be spent continuously to arbitrate write access and keep the network honest (cf. “proof of work”).
Local-first cooperation aims in the opposite direction. By keeping all decisions local and avoiding consensus wherever possible we remove the need for mechanisms like “proof of work”. Every device — as configured by its owner or admin — decides for itself which inputs to trust.
Another component to this is that the existing edge devices are used to run business logic, store data, and transmit events. Additional cloud infrastructure is reduced to those functions that cannot run locally, which means less servers are running and less bits are pushed through the Internet backbone links. And it means that the edge devices are used to a higher degree, maximising the usefulness of their initial production and ongoing operational cost.