Difference between Be at each other’s throats and Cut each other’s throats

be at each other’s throats—be arguing violently; be very angry with each other:

• We cannot deal with tomorrow’s problems if we are at each other’s throats over economic issues.

cut each other’s throats—harm each other’s interests, especially because of fierce competition:

• They are cutting each other’s throats in their eagerness to finish the work first.