We know that any known element is defined by the number of protons in its nucleus (which is the same as the number of orbiting electrons).
We can define isotopes as the atoms of the same element but that have a different number of neutrons in the nucleus. The correct statement of the difference between stable isotopes and unstable isotopes is:
"The difference between a stable isotope and an unstable isotope of an element is that the unstable isotope has a nucleus that decays spontaneously, is radioactive, and can be transformed into an atom of another element"
Particularly we can define two of these, the stable isotopes, that can remain as they are for a lot of time, and the unstable isotopes, that have more neutrons in its nucleus than a stable isotope, and because having those extra neutrons in the nucleus needs energy, eventually the isotope will experience a spontaneous radioactive decay, which "breaks" the nucleus in different ways, and, in some cases, generates different elements in the process.
Then we can conclude that:
"The difference between a stable isotope and an unstable isotope of an element is that the unstable isotope has a nucleus that decays spontaneously, is radioactive, and can be transformed into an atom of another element"
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