Those are two different Bluetooth profiles (wouldn't it be nice if every manufacturer used the same profile?). Headset is generally used for phone headsets and handsfree started as a car kit/BT speakerphone solution but several Nokias use it for all BT products, even headsets.
The SE uses headset profile, and it's just that the phone sends audio out for call-related stuff only, not system sounds such as voice memos and alerts.
The headset should work with the X30 and notebooks with Bluetooth, yes. In fact, if you read our review of the X30, you'll see we tested the Jabra 250 with the X30.