This. As far as we're aware, physics doesn't understand narrative, and doesn't see any difference between killing a person, moving a gun or even disturbing a speck of dust: all entail things being in the wrong place compared with the original timeline.
You might expect some similarities on a macro scale regardless: perhaps if you kill baby Hitler, Germany can still be expected to end up with a different right wing leader who invades Poland, perhaps even assisted by people who were prominent Nazis in our time, and maybe even loses to the same allies for the same reasons. But on a micro level the differences are huge: the dates will be different, people dying will be different, and the rest of the twentieth century will be different. A century of different atoms bumping into different atoms, different sperm are getting to the front of different queues, and different people being influenced into different decisions results in a different world. Our would-be time traveller isn't even born, never mind motivated to look for Ms Schiklgruber's illegitimate child.
You might expect some similarities on a macro scale regardless: perhaps if you kill baby Hitler, Germany can still be expected to end up with a different right wing leader who invades Poland, perhaps even assisted by people who were prominent Nazis in our time, and maybe even loses to the same allies for the same reasons. But on a micro level the differences are huge: the dates will be different, people dying will be different, and the rest of the twentieth century will be different. A century of different atoms bumping into different atoms, different sperm are getting to the front of different queues, and different people being influenced into different decisions results in a different world. Our would-be time traveller isn't even born, never mind motivated to look for Ms Schiklgruber's illegitimate child.