Hi
There are two different versions of Apple Watch Series 3 (not iwatch):
For the best performance from your iPhone and (all models of) Apple Watch, including the most power-efficient communication between them, Apple recommends keeping both Bluetooth and Wi-Fi permanently enabled on your iPhone.
All models of Apple Watch can be used to send and receive texts and to make and receive calls when your iPhone is nearby and, potentially, other certain other circumstances (see below):
Apple Watch Series 3 (GPS)
Apple Watch Series 3 (GPS) models do not have built-in cellular capabilities. Any data consumed by it is consumed either via the paired iPhone (including Wi-Fi and cellular data) or via a direct connection between the watch and a compatible Wi-Fi network.
When consuming data, Apple Watch will aways first try to connect to the paired iPhone via Bluetooth.
If the iPhone is not available, it next tries to connect to a compatible Wi-Fi network:
About Bluetooth, Wi-Fi, and cellular on your Apple Watch - Apple Support
Wi-Fi can only be turned off on these models by enabling Airplane Mode.
A separate cellular plan for the Apple Watch is not required.
Apple Watch Series 3 (GPS + Cellular)
In respect of data usage, Apple Watch Series 3 (GPS + Cellular) also always first tries to use the Bluetooth connection to your iPhone (which does not require a separate plan for the watch) or, in the absence of that, any available connection to a compatible Wi-Fi network.
If neither of those is available, then Apple Watch Series 3 (GPS + Cellular) has a built-in cellular capability that, under certain circumstances, can enable certain features, which are not available on GPS-only models, to remain available when the watch is used without the iPhone nearby.
In order to be able to use the built-in cellular feature, you would require a carrier service plan for your iPhone that specifically includes support for the Apple Watch, including the carrier first activating the device on the plan:
If desired, Wi-Fi can be turned off on these models via Control Centre in order to force the watch to connect via cellular, when away from the paired iPhone:
Use the Control Center on your Apple Watch - Apple Support
Apple Watch Series 3 (GPS + Cellular) can also be used without enabling the built-in cellular feature, in which case it functions like a GPS-only model and can be used in conjunction with a service plan for iPhone from any carrier, with no need to activate the watch on the plan.
Both
The 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