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US spec models use a proprietary connector for charging. Europe has a standard, it used to be type 2/mennekes and now is ccs2 which US models do not have.
OP send me a message and I'll point you in the right direction. I've had my US spec 3 in Germany for almost 2 years now and have had to rely on a 3rd party adapter for supercharging.
There are indeed two cables. Type 2 and CCS 2. The US plug is smaller and basically a different pin layout than type 2 which is why this adapter can work. The original s and x that were sold in the EU came with a type 2 port, Tesla now offers an adapter or retrofit for those older cars.
If your car has the Tesla proprietary port that is used on North American cars and you want to Supercharge in Europe, you can buy this adapter. It will allow you to use the V2 Superchargers, not V3 which can only be used with Tesla cars with CCS ports or CCS adapters.
Though not as fast as Supercharging, there is also the CHAdeMO adapter. One interesting thing about CHAdeMO is that the plug, socket, and electrical protocols are identical worldwide.