ax to grind vs rough-and-tumble

ax to grind

• A grudge or grievance, with implications of confrontation. 

• A proposition or point of view to advocate, especially motivated by self-interest. 

rough-and-tumble

• Rough activity; fighting or brawling; a fight. 

• An environment of rough activity 

• A person who characteristically engages in such activity 

• active, vigorous and rough, with the possibility of harm 

• highly competitive 

• Engage in rough-and-tumble activity