If you have the GPS only Apple Watch, then it will use your iPhone's radios, as long as your iPhone is nearby.
If your carrier supports WiFi calling, AND you have it enabled on your iPhone, AND you enable it on your Apple Watch, then as long as you are in range of your home WiFi, the GPS only Apple Watch can make a WiFi enabled call.
If you are away from home, and away from your iPhone, then the GPS only Apple Watch cannot call anyone.
A cellular Apple Watch can of course make an emergency services call without an iPhone or your home WiFi being nearby (assuming you are within range of a cellular tower).
As a bonus, a cellular Apple Watch that HAS NOT been added to a carrier service, can still make Emergency services calls (911, 999, etc... as per the area of the world where you live). Of course it cannot call your backup emergency contacts, as that is a regular call, and you cannot make those without a cellular plan in place.
NOTE: The Apple Watch pairs to your iPhone, and shares your iPhone's phone number. Your iPhone needs to be using a carrier that supports the Apple Watch. Here is list of carriers
https://www.apple.com/watch/cellular