Yeah the comparisons between the US and Europe are always a stretch just because of the size and heterogeneity of the US. You can't compare the US to the UK because you also have to include Bosnia and other places that are poorer and where life is cheaper.
The vast majority of gun violence in the US is domestic (where it doesn't particularly matter if a gun is used or not) and gang violence. The random shootings like we hear about in the news are statistically rare in a population of 330 million people but get huge amounts of attention.
You're right. Because of the bosnias of Europe I added the modifier "by and large". And it's probably also true that some parts of the USA are much more violent than others.