Tesla S & X models charge through a proprietary Tesla plug that is electrically (but not physically) compatible with the North American J1772 charging standard. Tesla cars come with a small J1772 adapter to allow charging from any J1772 public or home EVSE.
Model S/X also come with a Gen 1 (pre spring 2018) or Gen 2 (post spring 2018) Mobile Connector that allows charging from almost any type of North American plug (via Gen 1 adapters or Gen 2 adapters) and comes standard with an adapter for a household 120V 15A receptacle. You can purchase adapters for other receptacles including various 240V receptacles.
All Tesla cars have the ability to charge from high speed D.C. charging stations, but in some model configurations, this D.C. charging ability is an extra cost option. If D.C. charging is enabled, Model S & X can charge from any Tesla Supercharger at power levels up to 250 kW (typically 300-500 miles of range per hour). Also, if D.C. charging is enabled, you can purchase a Tesla CHAdeMO adapter to charge from any CHAdeMO fast D.C. charge station at up to 50 kW of power, or around 140 miles of range per hour. D.C. charging speeds are variable due to a number of factors including: how hot the charger/cable is, how hot/cold the car battery is, whether the charger current is paired with another stall, and how full the battery is.
Tesla cars come with a built in charger capable of A.C. charging anywhere from 32A to 80A (or about 23 to 58 miles of range added per hour) depending on your specific car. Since Tesla doesn't have model years, and capabilities have changed several times, and different charging options were offered at different times, there is no easy way to tell what a particular Model S or X can charge at. Suffice it to say that any Model S or X can charge to full overnight, and some Model S or X have higher speed chargers, that when paired with a Tesla Wall Connector, can charge fairly quickly to allow owners who drive their cars around town a lot (say a real estate agent or local outside sales person) to get a reasonable increase in charge during the day.
In the past, Tesla recommended that new owners install a NEMA 14-50 receptacle and use their included Mobile Connector to charge their car. While that is still an option, I personally recommend that new owners instead purchase a Tesla Wall Connector and leave their Mobile Connector in their frunk or trunk. The Wall Connector is more robust, allows for circuit sharing should you get a second EV, and makes sure you'll never forget your Mobile Connector when going on a trip. Note that Tesla no longer includes a NEMA 14-50 adapter in new cars, you need to purchase that from their online store.
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