The 'UK v US thing' is a valid comparison to make as the two nations encompass both ends of the spectrum when it comes to guns.
We don't deploy armed police generally to people armed with knives. In the US though, every time you encounter the police, whether you're armed and threatening or simply have faulty break lights on your car, you are met with an armed officer. So the potential for someone to get shot and killed is exponentially higher in the US than in the UK.