It basically boils down to everything, but for example the post-Dunblaine total gun ban that US gun control advocates point to was actually a total ban on handgun ownership - when they've been pushing heavily on the idea that rifles are obviously more dangerous than handguns and that it's nuts for them to be less heavily restricted. It's basically only the pro-gun side who seems to argue handguns are more of a problem, even though they do seem to be overall in the US too. (It'd also mean no more private armed security for left-wing Hollywood celebrities, an idea prominent gun control supporters dislike.) They get close sometimes for a moment, for instance the UK does have stricter gun licensing than the US - but we also let 14 year olds get gun licenses to create a culture where guns are seen as tools which can be used by those who show they can be trusted with them, something which would be unthinkable to US gun control supporters. (Until quite recently I don't think there even was a lower age limit.) They also like to point to scary-looking black small-calibre bolt action rifles as examples of guns too dangerous even to be sold to 18 year olds; as far as I can tell that's typically what a 14 year old would use as their first gun both here and in the US. It's outside my and most UK resident's area of personal experience of course, which is one big difference from the US.

Honestly, a lot of the UK stuff seems to almost have more in common with US gun owner culture than their anti-gun campaigners, though obviously organisations like the NRA would not be happy at all with UK levels of gun ownership restrictions. The fact that self-defence is not a valid reason to have a gun or any other weapon here would also be unacceptable to pretty much everyone in the US from what I can tell, not to mention unconstitutional. (This includes stuff like pepper spray.)