Yes, they are related, and I'm guessing that the larger carnation plants will have a larger root system that would survive a freeze better than the dianthus.

But you are gambling with most potted plants if leaving them out during an extended severe freeze.

They are very closely related and really the only thing that would prevent their overwintering is less than ideal drainage. Dianthus of any kind really prefer fast drainage and often our winter soils just remain too soggy for them to be happy - they are certainly plenty cold hardy.

If you are growing them in containers, just make sure you use a good quality, fast draining potting soil (no Miracle Gro!!) and keep the containers out of the worst of the direct weather in winter. And depending on container size, you may want to shift them into the garage during any Arctic blasts that may come our way this winter.

After reading up on Carnations, I was surprised by the amount of variability.
I have some old fashioned 'Pinks'. The fragrant ones. My son took some over to Spokane a few years ago. Much to my surprise they have done well, showing no winter damage whatsoever.
Here's some of mine in front of a Cryptomeria J., 'Nana'.