Can atoms of two different elements have the same number of protons?
Atoms from two different elements may have the same number of neutrons, but never the same number of protons. The number of protons is unique to the element and represents the atomic number.
For example, you can look at radioactive decay. Uranium-238 decays and loses alpha and beta particles. When it loses and alpha particle, it loses two protons in its nucleus. At this point, it is no longer Uranium, rather, it is Plutonium