Lithium ions are rechargeable batteries; lithium primaries are non rechargeable, high performance batteries.
Apple air tags use lithium primaries, but I suspect airlines do not care and both kinds are banned (from loaded-in-device-in-baggage flight).
FAA specifically allows non-rechargeable small Lithium cells if in equipment in checked baggage. However, the table on the second pages says that small battery/cell spares are not allowed in checked baggage. “Lithium metal batteries (a.k.a.: non-rechargeable lithium, primary lithium). These batteries are often used with cameras and other small personal electronics. Consumer-sized batteries (up to 2 grams of lithium per battery) may be carried. This includes all the typical non-rechargeable lithium batteries used in cameras (AA, AAA, 123, CR123A, CR1, CR2, CRV3, CR22, 2CR5, etc.) as well as the flat round lithium button cells.” — https://www.faa.gov/hazmat/packsafe/resources/media/Airline_...
Note that lithium itself is a very volatile metal (it starts burning in contact with water, for example).