Apple Watch Series 3 (GPS + Cellular) is not locked to any specific carrier and has a built-in eSIM that copies information from the iPhone's SIM card and uses the same phone number as the iPhone.
The built-in cellular features require a carrier plan for your iPhone that specifically includes support for the Apple Watch, including the carrier activating the watch on the plan.
Currently supported carriers are detailed here:
Apple Watch - Carriers - Apple
Notifications for calls and messages
How notifications for messages are delivered depends on the status of your devices and your settings. With Wrist Detection enabled, in order to bring notifications to your attention as soon as possible:
- If your iPhone is unlocked, then you will receive notification alerts on your iPhone instead of on your Apple Watch.
- If your iPhone is locked or asleep and your Apple Watch is unlocked (regardless of whether the watch display is asleep or awake) and on your wrist, you will receive notification alerts on your watch.
- If your Apple Watch is locked or has Do Not Disturb enabled, then notifications will go to your iPhone.
Alerts for incoming phone calls are delivered to both devices.
Notifications on your Apple Watch - Apple Support
Functions that are available on your Apple Watch when it is away from your iPhone depend on various factors including:
Features and requirements that apply under various circumstances are detailed here, including within the footnotes:
How to use your Apple Watch without your iPhone nearby - Apple Support
Apple Watch Nike+
Apple Watch Nike+ Series 3 models feature include a Nike Band, exclusive Nike watch faces (along with the standard Apple Watch watch faces) and closer integration with the Nike+ Run Club app. The Nike watch faces include a permanent complication / shortcut for launching the app.
Otherwise, the models have the same internal hardware features as the comparable model (case material and GPS or GPS + Cellular version) and the same standard features of watchOS.
The Nike+ Run Club app can also be installed on other Apple Watch models.
Note that Nike+ models are only available in aluminium case versions, with Ion-X glass. Other Series 3 models offer the option of a stainless steel case and sapphire crystal (or ceramic case, for Apple Watch Edition).