Does this require all devices to be on the same wifi network?
No. both devices have to be signed into with the same Apple ID and be connected via Bluetooth.
It says on the apple site that both need wifi.
Connect all your devices to the same Wi-Fi network.
All devices must be on the same Wi-Fi network.
Bluetooth 4. If you're not seeing it your Mac may be too old.
I'm trying between an iPhone 5 and iPad air. They can't see each other over Bluetooth.
They can when personal hotspot is on but even then handoff still doesn't work so I think it's a problem with handoff or my iCloud account which does keep asking me for my password.
http://youtu.be/JDIoFOF8BWg
This video explains what uses what ie Bluetooth for handoff wifi for phone calls.
So far, all my devices/computer work in harmony with each other. But the phone rings on all three with different ringtones!