Sure, there is a massive difference. I think society should support the former, but not the latter.
But those arguing for socialised medicine aren't arguing that society should help the gunshot victim, they're arguing that the money to do so should be coerced from members of society. That coercion is morally wrong, regardless of how worthy the recipient is.
Also, if societal support were voluntary, people could choose between supporting the gunshot victim or the bank.
No, "coercing" money from people isn't morally wrong, it's part of the social contract. I'm a pacifist, but I still recognize that the sort of society left undefended doesn't last long so I pay the share of taxes that go to the military. Trade becomes difficult without roads, so every member of a vibrant economy pays for the infrastructure necessary to conduct that trade. I extend that to healthcare. A sick populous is less productive and less desirable.
Also, and this is a serious question: what is your definition of pacifism, that it allows for coercive funding? I assume here that you support the arrest and jailing of those who refuse to pay tax (and their probable death, should they refuse to be arrested either).
I don't see how anyone can be in favour of one, but not the other. In practice, though, most people favour one or the other, but not neither of both.