The zigbee standard allows for multiple “profiles,” and they can’t all talk to each other. They don’t even use the same addressing standards.
SmartThings uses the zigbee home automation (ZHA 1.2) profile. If the device is also certified for that same profile, then there’s a good chance that it can be made to work with SmartThings.
But if it uses one of the other profiles, including a manufacturer proprietary one, it could still be a certified zigbee device, but might not work with SmartThings.
So that’s why people are asking for the manufacturer and model number. That way we can find out what profile it uses and know where we’re starting from.