Tesla has its own charge connection, but they usually also give their buyers the J1772 adapter as well. Tesla needs its own connector because of their supercharging network being exclusively for Tesla. The J1772 is the only connector for the smart and MOST other EV vehicles, as that has been universally adopted. There is also a Chademo (no I am not going to mix the upper and lowercase) connection that is unique, but the smart EV doesn't really need that anyway. Level 2 suits the car just fine for performance reasons.
There are technically other chargers out as well, but most of those are for older electric vehicles such as the old Saturn EV1 and other older EV vehicles from well beyond 10 years ago at this point.