I think the universality of Bluetooth lies behind its ability to connect different devices. More advanced features are device dependent.
This can be explained in your example: the HBH-15 managed to successfully connect to your Nokia 8910 because both use Bluetooth and Bluetooth is for connectivity. I think the headset button for the voice dialing feature is Ericsson (or SonyEricsson) specific since it's an product designed to bring maximum functionality to phones. I don't know but my own theory is that using the headset button goes beyond Bluetooth - it will only work with specific phones.
I'd very much appreciate anyone correcting my information on this because I've been reading about Bluetooth and want to learn more about it.