The watch vibrates for all types of notifications (calls, messages from various apps, notifications from e.g. news apps, reminders, etc.). This must be set in the Withings app under Devices. There you can select the apps whose notifications are to be forwarded to the watch. In the watch itself, you can then mute everything if you want silence ("do not disturb" mode). With the iPhone, the night mode ("do not disturb" function in the iPhone) also blocks all notifications to the watch.

Mine also vibrates when I receive a call. But you can mute it

No, only when a message is received