Yes. They are the same products with different names for different markets worldwide. In the UK we have Lynx, but in other countries it is called Axe.
Sometimes this is done in order to prevent embarrassment ("a lynx" might be a big cat to us Brits, but in a foreign country it might be a swear word), other times is is a historical artefact. Sometimes the brands unite in the name of global harmony (a marathon became a snickers, as that's what everyone but us called it). Lynx wants to be a premium brand in the UK (with trendy adverts and a premium price relative to own brand lines) whereas in other countries it is viewed as an entry level product. This may be why there has not been name harmony so far. Some companies that export Lynx (as "axe") then re-import it, much like imported cars, because it is sold more cheaply to overseas suppliers. We end up with the mad situation that some call rip-off Britain, where it is possible to buy a product that has been shipped abroad, then brought back, more cheaply than one that has come through a UK supply chain, beacuse the UK suppliers pay a higher price at the factory gate.