Most charging cable have a special "head". This is the part that connects into your car. Majority of the cable heads in the USA are "SAE J1772" type. The plug or head is used by Tesla, Honda, Nissan, Ford, GM, and others.
If your Tesla cable doesn't have the SAE J1772 head or plug, you can buy an adapter here.
A word about Level 1, Level 2 and Level 3 chargers:
a) Level 1: this is the 120-volt power at your home. It's the slowest way to charge your Tesla. The plug for this looks like your regular home plug (you know, the on that you use to charge your iPhone)
b) Level 2: this is a 240-volt plug. It would look like the 2nd one in the above image. This would be most likely in your garage. If you don't have 240 volts you can upgrade your house to support it.
Find beautiful used Tesla cars for cheap here.
TeslaCarSearch.com is an independent organization and is not affiliated with Tesla Motors, Inc. or its subsidiaries. TESLA, TESLA MOTORS, TESLA ROADSTER, MODEL 3, MODEL S, MODEL X, ROADSTER, SEMI, TESLA SUPERCHARGER and the “TESLA,” “T” and “TESLA and T in Crest” designs are trademarks or registered trademarks of Tesla Motors, Inc. in the United States and other countries.