I'll give a quick summary of the non-premium versions as such:
FreeSync - to my understanding doesn't have many if any requirements other than variable refresh rate support. Older monitors often had limited working range. e.g. I have a 4k FreeSync display which from memory only works between 50-60 Hz.
G-sync Compatible - this seems to be the new normal as we move beyond original G-sync. To obtain this certification, there are image quality requirements that have to be met, as well as a minimum range of 2.4x between min and max supported fps.
G-sync (original) - uses additional hardware which allows the variable refresh rate to work down to 0 fps. Has image quality requirements. Downside was the extra cost in implementing this in monitors.
Good gaming displays now should be G-sync Compatible certified, and also works with FreeSync. No cost difference in that sense. There may be cheaper FreeSync only displays but they may be lower image quality.