But what is the difference between them?
An overdrive-pedal creates the gentlest kind of overdriven guitar-sound. It emulates the sound of an overdriven power-amp. Especially with low gain the signal stays almost clean and starts to overdrive lightly when you dig in harder.
But of course you can also create a crunchy guitar-sound by using an overdrive-pedal.
The so-called soft clipping is a distinctive attribute of overdrive-pedals.
By rounding off the amplitudes of the sinus curves of the audio-signal in a gentle way the soft clipping creates the overdriven sound.
Before it becomes far too technical I would like to explain things like this: Soft-clipping mostly is created by diodes in the circuit of the transistor. It is possible to connect several diodes in parallel to reduce the compression. If the number of diodes is odd the clipping of the sinus curves will be asymmetrical.
In contrast to the overdrive-pedal the distortion-effect emulates the overdriving of the preamp. This is created by a so-called hard-clipping which cuts off the amplitudes of the sinus curves of the audio-signal. This leads to a more intensive overdrive-sound.
The diodes by which the hard-clipping can be realized are grounded behind the transistor.
But the same applies here: a larger number of diodes brings up the headroom, an odd number of diodes creates an asymmetrical clipping while an even number leads to a symmetric clipping of the signals amplitudes.
While the overdrive-effect frequently adds the wet to dry signal and by this maintains the attack, the distortion- effect often only sends the wet signal.
Overdrive-effects as well as distortion-pedals are commonly either based on transistors or an IC. The technical implementation of an effect-pedal based on ICs is quiet easier and although many pedals, like for example all Tubescreamers, are built-up like this, in my opinion the discrete construction with a transistor creates a more dynamic overdrive- sound.
The fuzz-pedal creates the most extreme kind of overdrive. The effect of a fuzz sounds like the extreme overdriven preamp combined with a power-amp that also is extremely overdriven. Sometimes it almost produces the sound of a broken amplifier.
Almost at all times the signal of a fuzz-effect is amplified by several transistors. This leads to an extreme distorted signal that finally does not sound like a guitar anymore.
Attack and dynamic will be greatly reduced. But this does not mean that a fuzz no right to exist. Because of its extraordinary sound the fuzz mostly is played into an amplifier that is already overdriven.
Last but not least
Of course there are mixed types and exceptions. The Keeley Fuzz Head for example is supposed to sound like a fuzz that is played into an amplifier that is almost overdriven.
Like mentioned above, the compression of an overdrive- or a distortion-pedal depends in a decisive way on the diodes.
Many guitarists start the modification of their overdrive pedals by changing the IC (which sometimes of course makes sense). But I think it is more interesting to experiment with different manufacturers or varying numbers of clipping-diodes to adjust the compression or the character of overdrive.