Are we to assume the Intentional Homicide and the Assault Cases are separate from each other and not one subtracted from the other?
as a rule
If so, then couldn't we extrapolate that although the UK has higher assaults, they don't end in the death of victim?
And with that said, there'd be two views: "The UK is more violent because they have a ban on guns" versus "The UK would have more instances of deaths from violence were there not a ban on guns"
not quite. Even when UK had laxer gun laws than the US, the same situation existed. Whatever reason, using a gun was not considered "cool" to UK criminals. Other than a few criminal gangs, that still holds true. They tend to use machine guns more than we do. Depending on the size of the knife, caliber of the gun, and range, knives can be more lethal than guns. A kitchen butcher knife is more lethal than a .25 ACP and certaily more lethal than any gun using "armor piercing" ammo.
And all said and done, Japan - a significantly smaller country, area-wise, with an exceedingly dense population, is among the top 3 least violent countries even with significantly fewer guns than either? (Japan has .6 guns per 100 capita, UK has 6.2 per 100 capita, and the US has 88.8 per 100 capita)
You are assuming that the trigger pulls the finger, or that a gun is like a ring in a fantasy movie. Of course, those only count legal guns. They don't count those owned by the Yakusa who smuggle them from illegal factories in Cebu or make their own in Japan. I lived in Japan for over three years, it has nothing to do with guns. Their society is organized around community, not the individual. there is almost no wealth inequality. Of course, their legal system make fair trials almost impossible. Illegal searches and forced confessions are allowed in court. There is no right to council nor jury trial.