as true as 'get something that sounds good to you" might be, it isn't that helpful to the OP if he doesn't yet have the vocabulary to articulate what sounds good to him, and hence choose the right pedal based on other people's descriptions.
If it is a general question about why one box is classified overdrive, another distortion, another fuzz, I would agree with the continuum you suggest that distortion is generally 'more' than od, but fuzz is a slightly different beast. Thing is there is such a range of distorted tones that it is very hard to generalise any more than that.
Instead I would suggest trying to break the sound down into 3 main areas:
1. compression - how flat and sustainy is the sound (think santana)? For an uncompressed but overdriven rhythm sound listen to how long the mangled inter-modulation lasts after each strum - its a bit like setting the length of a reverb, there is a decay time which is just right.
2. Tone - how grainy or smooth is the sound? you get a grainy, raw overdrive when you distort upper mids and treble. If you roll back the guitar tone pot and just distort the fundamental, you get the overtones from the clipping process, which can sound very smooth (i call this a saturated sound.) Think Brian May, or some of satch's lead sounds.
3. Gain - how much actual drive is there? How much of the sound is still down to the guitar, and how much is down to the clipping process?
these are all interrelated, but identifying the different aspects of the sound might help you to get where you want to be. Most od pedals have at minimum a gain, vol and tone knob and you can learn a lot just from playing with these (whatever pedal you might already have - it doesn't matter too much) and your guitar tone pot.
If there are any guitar sounds on recordings that you wonder what type of pedal might get you there I for one would welcome some discussion on it. I'm sure there are plenty of people here who can offer suggestions and I'd love to hear and learn from those more knowledgeable and experienced in these things.