Question

Is the prohibition on eating carcass meat an object-based prohibition or a person-based obligation?
What’s the difference? Seemingly, whether I am commanded not to eat the carcass, or whether carcass meat is something that cannot be eaten by me (object-based), it comes out to the same thing. If there is a ball that is obligated to pass over every wall, then every wall is obligated that the ball pass over it. So is the whole difference just what the command focuses on first?
If so, what is the difference between a vow that takes effect on a commandment and an oath that does not take effect? I clash with the command in the same way either way—the wording is different—but I’m saying that I’m not obligated to perform the commandment. Why would the Torah allow that?