For SMS, your paired iPhone must be able to receive the SMS and must be connected to the Internet. Your Watch must also have an Internet connection, but it doesn’t need a cellular connection. However, so long as those conditions are met, the Watch and the iPhone can be on opposite sides of the planet. (Same for sending as receiving.)
As best I know, the only Watch plans you can get are add-ons to existing iPhone plans. Whether this is a technical limitation or a marketing one, I’ve no clue.
It’s worth noting that SMS is one of the few, and perhaps the most annoying, features that requires an actually-on iPhone. Next in line would be some 2FA systems. There are also a few third-party apps that just use the Watch as a front-end to the iPhone and require the Watch to be connected directly to the iPhone via Bluetooth or WiFi; for example, the ReSound hearing aid app works that way.
Other than those small caveats, you can use a cellular Apple Watch entirely independently of its paired iPhone, even when the iPhone is dead as a doornail. You can make and receive phone calls, access voicemail, send and receive iMessages, email, ApplePay … the works.
I’m not shy about leaving home without the iPhone — and, when I do have it with me, it’s often buried in a backpack and not in my pocket; I’m often quite happy using my Ultra for most smartphone-type things. And it was an absolute godsend for a few days when my iPhone was, indeed, dead as a doornail. Of course, I’ll break out the iPhone for its camera, or to read something, or for DuoLingo, or the like. Basically, the iPhone is, for me, a mini tablet with a great camera, and the Watch is my smartphone.
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