Each element has a unique number of protons. This unique number is known as the element's atomic number. All atoms of a given element have the same atomic number. For example:
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Carbon atoms have 6 protons, so the atomic number of carbon is 6.
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Hydrogen atoms have 1 proton, so the atomic number of hydrogen is 1.
On the other hand, as the atoms of different elements have different number of protons, they also have different atomic numbers. If one atom has 18 protons, and another atom has 19 protons, we can conclude that these two atoms must be from different elements. In essence, an element's atomic number, like your social security number, serves as its "numeric identity."
Notice that all the elements in the Periodic Table are arranged in order of increasing atomic number, and this also increasing number of protons.
Just as the atomic number of an element represents the number of protons in that element, it also represents the number of electrons in that element. Therefore, all (neutral) atoms of a given element have the same number of electrons as protons. For example, all carbon atoms have 6 protons and 6 electrons, and all hydrogen atoms have 1 proton and 1 electron.