EDIT: Put simply, potential difference is the work done by electrostatic force on a unit charge, while EMF is the work done by anything other than electrostatic force on a unit charge.
I don't like the term "voltage". It seems to mean anything measured in volts. I'd rather say electric potential and electromotive force.
And the two are fundamentally different.
Electrostatic field is conservative, that is, over any loop $l$ we have $\oint_l \vec{E}\cdot\mathrm{d}\vec{l}=0$. In other words, the line integral of electrostatic field does not depend on the path, but only on end points. So we can define point by point a scalar value electrostatic potential $\varphi$, such that
$$\varphi_A-\varphi_B=\int_A^B \vec{E}\cdot\mathrm{d}\vec{l},$$
or
$$q \left( \varphi_A-\varphi_B \right)=\int_A^B q\vec{E}\cdot\mathrm{d}\vec{l},$$
so $q\Delta\varphi$ equals the work done by electrostatic force.
In pratical application, electrons (and other carriers) flow in circuits. Since electrostatic field is conservative, it alone cannot move electrons in circles; it can only move them from lower potential to higher potential. You need another kind of force to move them from higher potential to lower ones in order to complete a cycle. This other force could be chemical, magnetic or even electric (vortex electric field, different from electrostatic field), and their equivalent contribution is called electromotive force.
$$\mathrm{E.M.F.}=\int_\text{Circuit} \frac{\vec{F}}{q}\cdot\mathrm{d}\vec{l}$$
A Faraday cage need not be a continuous conductor — you can make a reasonable Faraday cage out of chicken wire. The rule of thumb is that if the gaps in the conductor are small compared to the wavelength of the electromagnetic wave, the wave "won't notice" and the conductor will appear continuous; if the gaps are bigger than the wavelength, parts of the signal can pass through the cage without interaction. So a chicken-wire Faraday cage could be a good blocker of meter-scale radio waves, but would definitely be a poor blocker of millimeter-wave radio.
X-rays and gamma rays have wavelengths comparable to or smaller than the spacing between atoms in a metal, so even a solid piece of metal "looks like" a chicken-wire fence with lots of gaps.
An alternative explanation (which isn't as different as it might seem) is that radio waves can transfer energy to many of conduction electrons at once, making them slosh around. But there aren't any high-frequency collective motions for bound electrons in the conductor, so x-rays and gamma rays tend to excite single electrons and to give them enough energy that they essentially become free particles. (This is "Compton scattering"; photons above 1 MeV can also lose energy by creating electron-positron pairs.) Since the electron motion isn't collective, it doesn't really matter any more whether the electrons were conducting or not beforehand, and so conductors don't really make better shields for x-rays and gamma rays than similarly-dense insulators.
Best Answer
It can be a little confusing because there are two conventions.
The modern convention is to distinguish x-rays from gamma rays by how they are produced. X-rays are produced by electron energy transitions, typically inner orbital transitions, whereas gamma rays are produced by electromagnetic transitions in the nucleus.
Usually, gamma rays have shorter wavelength (and therefore higher frequency and energy) than x-rays, but not always. Some radioactive processes release gamma rays with frequencies in the ultraviolet portion of the electromagnetic spectrum.
However, there is an older convention which distinguishes them by energy. This convention is still common in astronomy and astrophysics. From Wikipedia:
Here's a diagram from that article.
In both conventions, x-rays are electromagnetic radiation with wavelength shorter than ~10 nm (and hence energy ~125 eV) and EM radiation just below that energy is considered to be ultraviolet light. Here's another relevant passage from that Wikipedia article:
Bremsstrahlung is braking radiation. It is any radiation produced due to the acceleration of a charged particle.
A table of gamma emitters from Professor Peter Siegel's page on the California State Polytechnic University site lists the energies of a wide range of radioisotopes. The lowest energy in the table is that of Erbium-169, which decays by beta emission (with a half-life of 9.4 days) but some decays also release a gamma ray. The energy of that gamma photon is a mere 8 keV, well below the astronomical threshold of 100 keV. It has a wavelength of 0.155 nm, so a bit shorter than high energy UV, and at the low end of x-ray energies.