Question

all atoms of the same element have the same

Answer 1

Number of protons in the nucleus are what make atoms different from other atoms. For example, hydrogen has an atomic number of 1, which is purely a fancy way of saying it has 1 proton. That's why it appears at the top left of the periodic table. So if you just have a lone proton, it's the EXACT same as if you have a single hydrogen atom there. Since protons are positive they generally repel each other, so if they're held together in a tight, smaller nucleus then we call these different atoms.

The picture shows that although there are 4 protons in each box, there are 4 hydrogen atoms in the left box and 2 helium atoms in the right box. Weird, but this is what we are talking about when we distinguish atoms.