The difference is you are with Verizon and using Message+ app to make and receive calls on the watch directly (that only works on Verizon). OP simply wants to get notified when a call comes in to the phone, not watch and get a chance to reject or pickup from the watch. If you setup your watch to play phone audio on the watch via BT. When a call comes in to your phone. Your phone rings. Your watch gets a notification. You pick up the call from the watch, it will always play on the speakers of the watch regardless if you have a BT headset connection on the watch or not. You can't relay BT audio from one device (your phone) to another BT device (your BT headset or car audio) via the watch.
Before the new firmware update, I was able to do exactly what OP asks even if my watch is not the currently selected BT headset (the phone will be connected to either car audio or another headset) on my Nov edition watch. Right now, if your watch is not the currently connected headset for phone, you get no notification what so ever.