I don't own one, but a smart watch with "full android" is basically a stripped and compacted down android cell phone, strapped to your wrist and worn like a watch. Think of it as a carrier unlocked streamlined Android cell phone that can be activated with its own SIM card and cellular phone number. In order to shrink everything down they have to cut corners a bit. Smaller battery, less on board memory, slower CPU, no IR blaster, no USB-C, no headphone jack, no fingerprint scanner...etc. But you can place and receive voice calls via bluetooth headset or in many cases speaking into the "watch" itself and listening to its small speaker. You can www surf and send/receive text messages. All without being connected to a cell phone, because it has its own SIM card and line activation.
They generally also limit the number of frequency bands too I think... that will probably vary a lot from model to model. So depending on what carrier you prefer, you will have to make sure the frequency is supported on the "watch". Just like any other carrier unlocked phone.
But it can also function as a bluetooth/wifi cell phone accessory and sync with your android cell phone to receive notifications...etc. So you really don't have to activate a cellular line for one.
Heres an example:
Android Wear is a specific android based operating system for those watches that Google designates as "AW compatible". Not all smart watches that sync up with an Android phone, use Android Wear as their watch OS. Basically AW is a feature specific operating system for smart watches. Because its wearable-centered, it has things like heat rate monitor, step counters... and probably others I am forgetting.
Confused yet???... Its getting little more convoluted now because there are AW watches that can be activated with a SIM card. So these watches are still AW, and "wearable centric" but add cellular connectivity and activation with a SIM card. So they can stand alone, place/receive calls and text, and yet do not need to be connected to a cell phone "host".
These are just basic basic generalizations... it should be taken more case by case because the lines of distinction are blurring more and more.