So many comments are based on different understanding of local-first. For some it means no data on the server, allowing some claim it's better for data privacy (but what about tracking?). For others it means it works offline but data is also on the server and there is some smart syncing (e.g. with CRDT). Others speak of apps requiring no remote data and no network needed, though I find box-product to not be very explicit in describing such category.
Also there does not seem to be any commonly agreed definition for local-first or even offline-first. I would assume the -first suffix means there are other ways but one is favored. So offline-first would mean it works online and offline, while local-first means it stores data locally and also remotely, meaning some syncing happens for any overlapping area. However syncing requires network connection, so is there really a difference between local-first and offline-first?
Personally I would use local-only or offline-only for apps that do not require respectively access to remote data or network, the latter being a subset of the former. With these -only terms in mind, I then see no difference between local-first and offline-first.