For the most part, fire is is just gas that's red-hot.
If you get a gas really really incredibly hot it will turn into a plasma. You can tell the difference depending on how it reacts to light and magnetism. (a plasma is electrically conducting, and so is opaque, though being red hot anyway, this would be hard to test by trying to look through it (a laser might be useful, though)). You can bend plasma with magnetic fields, too.
There are many states of matter, but there are a few well recognized phases of matter.
There's the usual solid, liquid, and gas
But there's also (on the hot end), ordinary plasmas (when electrons are no longer bound to nuclei), and quark-gluon plasmas (when protons, neutrons, and their constituents are no longer bound together as nuclei)
On the cold end, there are Bose-Einstein condensates. These are gases so cold that the individual atoms all share the same ground state, and act as though they are described by one wavefunction like a giant atom.
As far as electricity goes, you can describe it at least theoretically as a gas of particles moving through an idealized African rainstick.