But there are huge differences:
1. Concealed and unconcealed carrying is not allowed. You have to transport your weapon in a very specific way, without ammo etc. Also anyone with a gun in public would trigger a police intervention within minutes.
2. Active military personnel are allowed to stored their gun at home, but almost nobody does that. Those who do get 5 bullets, in a sealed box. They're not allowed to open it, except in war. The seal gets checked every time you go back for service.
3. Storage of legal weapons at home is very strictly regulated. Loaded guns are basically forbidden, ammunition has to be stored separately etc.
4. If you don't have a very clean history, it's almost impossible to get the right to buy guns.
5. Automatic weapons are illegal.
PS: Those "facts" are from my memory, as I don't live in Switzerland anymore. Fellow Swiss users, if there's anything wrong please correct me.