Meg St._Clair wrote:
To expand a bit on Jonathan's answer, you can connect your phone to multiple BT devices as long as they are different kinds of devices. For example, you can't pair to two sets of headsets at once but you can pair to an Apple Watch, headset and a BT heart rate strap (as I do) all at once.
To further expand, you can PAIR two or more headsets to an iOS device (I have 4 headsets paired), but you can only CONNECT to one at a time to use it. The Watch is not paired in the usual sense; it uses Bluetooth LE (aka Bluetooth 4) which does not require pairing the devices; likewise for heart rate straps, Fitbit pedometers, Tile location trackers,etc. The limit on Bluetooth LE devices is 8 per device type.