Is the only absolute difference between types of light frequency? Probably a bad question but for some reason, it seems too simple in my head that anyone at home could theoretically create anything from radio waves to gamma waves by generating electrical signals at different frequencies. 
Say I had a electronic frequency generator that was able to produce a signal at any frequency, and for illustrative purposes, say there was a diode hooked up this generator that could receive its signals.
If it created a signal at $10^{12}$ Hz, the diode would give off infrared radiation.
If I increased the signal to $10^{20}$ Hz, the diode would give off gamma radiation.
I’m using this example just to emphasize my question, is frequency the absolute and only differentiator in types of light on the electromagnetic spectrum?
 A: Your question is a little confused at the end, but I think the answer to what you're trying to ask is "yes".  Names like infrared and gamma apply here to ranges that have been divided up for historical and practical reasons, but they do not denote something other then an electromagnetic wave within certain frequency ranges.  If you had the hypothetical device that you mentioned, then you could create waves of any of the types that you mentioned. (Although I know of no such single device that covers such a range.)
Also note that there can be more than one name for a particular range.  For example "radio" waves have different bands and those bands go by different names by country and by science / engineering discipline.  For example, K Band or X Band.
The "electromagnetic spectrum" would cover all frequencies by definition, so your device would not create something "outside" of the spectrum.  It might, I suppose, create a wave in a frequency range that has no conventional name.
A: There are no different types of light in the elementary sense. Whys should we distinguish types of light based on frequency or spin, as we don't do this for any other particle. 
A: 
[F]or some reason, it seems too simple in my head that anyone at home could theoretically create anything from radio waves to gamma waves by generating electrical signals at different frequencies.

I don't see how to easily create a device that vibrates at 10¹² Hz, not even 10⁶ Hz. Technologically, this is not as simple as it sounds.
As mentioned by @Brick, the "electromagnetic spectrum" includes all frequencies. What makes a wave "electromagnetic" is not the frequency but the nature of the phenomenon. In electromagnetic waves you have oscillations of electric and magnetic fields through space, and also a transport of energy while the wave propagates.
A: You asked a very reasonable question. The EM spectrum from gamma to infrared is the emission of photons from excited electrons and other subatomic particles:


*

*Bombardment of a nucleus with high-energy particles mainly produces X-ray photons. The kinetic energy is partly converted into photons.

*The annihilation between a particle and its antiparticle leads to two, three or rarer more then three photons, of which at least two are in the gamma spectrum.

*The ohmic resistance is nothing more than the emission of infrared photons and some photons in the visible spectrum by the zigzagging of moving electrons inside the conductor. Bending or deforming a solid leads also to the emission of infrared photons.

*Deflecting electrons in a magnetic field (Lorentz force) also leads to photon emission, this time of lower and lower frequency in relation to the slowing down (moving in a spiral) electron. 


Now let us create a radio wave by the technics I described above. This is impossible. The invention of wave generators and the use of antenna roads were the requirements for the production of radio waves. A lot of electrons are pushed inside the rod. All these accelerated electrons emit photons. But at the end a saturation of electrons (or of the absence of electron) occurs. The wave generator is responsible for the periodical change in the direction of flow of the electrons. As a result you get a periodical emission of photons which is the carrier frequency on which one tune the receiver.
Long speech, short story. Radio waves are modulated radiation with photons from infrared to gamma and by this they are technically part of the EM spectrum, but in a strong physical understanding, they should not. In physics this isn’t a point of discussion, but since you asked your question, this answer came into my mind.
The point is, that you can use even e very short rod, much much smaller the  calculated wavelength and you get a radio wave. With a terrible efficiency and signal, far away a sine wave. The photons inside  the radio wave depend from the accelerations of the electrons on the skin of the rod and in dependence from the power of the wave generator, the material and the shape of the rod, these photons could be from infrared to X-ray. I not recommend to be too close to a radar or a MF broadcast antenna.
