Yeah definitely, in the research community I am a part of we try to say “lithium-free” rather than anode-free but the later is more common in the literature. Even then it isn’t lithium free always just at assembly (and theoretically at 100% discharge if everything is behaving ideally).

It’s bad branding but essentially a lithium anode would be a metal film on a copper foil. As you charge the battery Li from the cathode would plate in the existing lithium which acts as a reservoir to compensate for any lost capacity due to natural aging. In an anode free configuration there is zero initial lithium, just bare copper (maybe with a coating or some other modification but the key detail is zero initial lithium on the anode. That is the primary source of gravimetric capacity increases in “anode free” cells since you can remove the weight of the lithium reservoir. This requires extremely high coulombic efficiency since there is nothing to compensate for any lost lithium.