Protons DO carry a positive charge.
The number of protons in a nucleus is the atomic number, which also determines the number of electrons the atom has, and defines which element we are talking about.
Atoms can have various numbers of neutrons as well as protons in their nucleus.
Neutrons are uncharged and different numbers of them in the nucleus of an atom are the different isotopes.
Different isotopes are still of the same element though and they have the same number of electrons and similar chemical properties.
Different isotopes of the same element do not have similar nuclear reactions though.
Some isotopes of an element are stable for a very long time, even immeasurably long, whereas others are not stable and can easy undergo nuclear reactions, (either fission or fusion).
This leads to nucleii with a different number of protons to the original, so new elements are produced as a result of these reactions.