It’s exactly what you said, it’s a carbon atom with 12 nucleons. [element]-[mass #] is a common way to define isotopes of each element. For instance, carbon-14 would have 6 protons and 8 neutrons. Carbon will always have 6 protons (because that’s what makes it carbon) so additional/reduced atomic mass will always be from changing the number of neutrons.
Electrons aren’t dignified in this notation, it tells you nothing about the electric charge other than the number of protons. When you involve electrons, you’re talking about ions, not isotopes. Isotopes can be ionic but not always.
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