No, all lithium batteries are not rechargeable. To help understand this concept better, let's talk about the difference between lithium batteries and lithium-ion batteries. Lithium batteries refer to what we call primary cell batteries that you can't recharge.
These batteries are very energy-dense and can store and emit power for long periods. They're great for watches, smoke detectors, and pacemakers–all of which need constant and continuous power. Nevertheless, once they're done, they're done, and must be disposed of.
Lithium-ion batteries, on the other hand, are rechargeable. We call this type of cell a secondary cell. This means that the lithium ions can move in two directions: from the anode to the cathode while discharging and from the cathode to the anode when recharging. Lithium-ion batteries are used for everything from earbuds to home backup power systems.