Of course, it also works on the move. You need 4g if you are only travelling with the watch without a connected phone and still want to use functions such as making calls.

This means that outside (i.e. not connected to Wi-Fi) to send messages or call people, it needs to be connected to your phone, which needs to be connected to the internet or have 4G. With the Apple Watch 4G, it doesn't need to be connected to the phone.