Answers to questions about terminology

What is the difference between "distortion" and "overdrive"? And "fuzz"?
Effectively none. "Overdrive" started as what you got when you put too large a signal into the input of an amp, causing the signal to be distorted at the speaker. You were "overdriving" the inputs. "Distortion" is the more generic term, and started when folks noticed that you could get a distorted sound from a little solid state amp that was VERY nonlinear. The terms have been used so interchangeably that there is no real difference, although some people will swear that only tubes being overdriven sound good, etc. Let them insist. It won't hurt much either way.

Boss and Ibanez seemed to define this difference with their pedals. The Boss OD-1 and Ibanez TS-9 Tube screamer "overdrives" are a smoother, less harsh sound than the DS-1 and SD-9 distortions.

The distortion pedals add more crunchy, gritty sound, whereas the overdrives add more smoothness and not as much distorted crunch. An MXR "distortion plus" is the definitive distortion pedal from the 1970s.

"Fuzz" seems to be an easier term to agree on a definition for. Pretty much everyone involved agrees that fuzz is a harder, harsher, and buzzier distortion than overdrive, and usually considered harder and harsher than "distortion" by itself. There is no real boundary on all this - it's just which words you want to use, no strict definitions.

What is the difference between "vibrato" and "tremolo"?
In strict musical terms, vibrato is a slight, cyclic change of the frequency of the note, while "tremolo" is a cyclic change in the amplitude of the notes. The amp and effects makers have used the terms interchangeably a lot, so for amps and effects, you cannot tell what you will be getting from the term.
If you dig into the raw math and do the fourier transforms, it turns out that there is not a lot of difference in the two for small modulations. For small amounts of frequency modulation, the actual sound produced is very similar.