Here, many different things are being mixed up... OBD, KWP2000, CAN... these unfortunately only have a limited connection to each other

.
So:
In Europe, there isn't actually any OBD or OBD2... instead, the EOBD or EOBD 2 variant is used. The difference is minimal, but important. The addressing of the diagnostic addresses is different.
OBD (regardless of the specific implementation) is a protocol, just like ODX or XCP. It is not tied to any particular interface or communication method.
There are OBD2 systems that use the CAN interface (which is most commonly used), but also those that use K-Line, VCAN, etc.
Regarding the communication method – that is, how data is precisely transmitted from the control unit to the tester via an interface – there are different types. Besides KWP2000 (KeyWord Protocol 2000), there is also UDS (Unified Diagnostic Services), for example.
Staying with the example of the Roadster (or smart), all smart models support OBD. Starting with the Roadster and CityCoupe (450 facelift), OBD2 is supported. This is either via CAN (starting with the Forfour) or via K-Line. From the W453 model onwards, UDS is used; before that, it was KWP2000.
Actually quite simple

.