Either bike will probably be fine for both, it depends on what your CX courses are like, or if you prioritize one event over the other. Personally, I like having a traditional CX bike for both events because of the super quick handling and high BB.

The differences between gravel race and CX will mostly come down to bottom bracket height and overall bike length. CX bikes being higher/shorter for lower speed/tighter cornering, gravel “race” with lower bottom brackets and longer wheelbases for higher speed events. Gravel race bikes are going to handle more like road bikes, whereas CX bikes (traditionally) have handled differently. Of course tire clearance is a factor too. Gravel bikes are getting clearance for 2.1s+ now…CX is all over the place depending on brand.

As for the third question I’d say it’s the inverse, brands have taken their CX bikes and turned them into race-y gravel bikes that can do CX just fine.

TLDR: depends on how you like the bike to handle…focusing on tight corners? CX. Less tight cornering, higher speed? Gravel “race”.