The phone can only be paired to ONE watch. There is a setting on the phone which says -
'Auto Switch' - Automatically connect to any paired Apple Watch when you put it on and raise your wrist.
If this setting is on, and you take off Watch 1 and put on Watch 2, Watch 1 is disconnected, and Watch 2 is connected automatically.
If this setting is on, and someone else puts on Watch 2, Watch 1 remains connected, Watch 2 is unconnected.
If this setting is off, and someone takes off Watch 1 or puts on Watch 2, nothing happens. Watch 1 is still connected, and Watch 2 is not connected
You can also manually connect and disconnect each watch if you want. But no more than 1 can be connected at the same time. Note this is NOT pairing/unpairing, both watches are still paired to the same phone, just one is connected and the other is disconnected.